First of all, shortening and combining prayers together in travel is a dispensation that Allah has granted Muslims to make worship easier. Almighty Allah is Most Gracious, Most Merciful.

Elaborating on the distance of Qasr and the modes of performing Prayer while traveling, we’d like to cite the following fatwa issued bySheikh `Atiyyah Saqr, former head of Al-Azhar Fatwa Committee, who states the following:

“Allah says in the Glorious Qur’an: “And when you go forth in the land, it is no sin for you to curtail (your) worship if you fear that those who disbelieve may attack you…” (An-Nisaa’: 101)
Fear of temptation mentioned in the verse is not the condition that warrants shortening prayers. This is according to the Prophet, peace and blessings be upon him, who considered this as a gift Allah has bestowed on His servants. Therefore, it is fitting for us to accept Allah’s gift.

As for the type of travelling that warrants shortening prayers, the scholars differ  in opinion on this. According to Zahirites, one is allowed to shorten prayers in any journey, whether the distance is long or short and even within three miles. They base this on the Hadith where Anas Ibn Malik, may Allah be pleased with him, says that whenever the Prophet, peace and blessings be upon him, set out on a journey of three miles or nine miles (this indicates doubtfulness on the part of the narrator, Shu`bah), he’d perform prayers of two Rak`ahs.

Imam Al-Qurtubi comments on this: “This does not qualify enough to be evidence, as it is doubtful. Even if we assume the authenticity of one of those two distances, it might be the starting point of the Prophet’s journey, which extended to more than three miles or more.”

Actually, the distance of a journey that warrants shortening prayers is neither clarified in the Qur’an nor in the Sunnah. The reason for this is that what was meant by the Arabic word “As-Safar ” at that time was well known to people of that period (the people first receiving the Qur’an). Besides, we know that leaving the house for a short errand is not considered as travelling in the lexical and literal meaning. But anyone who walks a long distance that takes three days is considered to be travelling and the same applies to a person who walks a distance that takes a day and night, according to Imam Malik.
this is based on the Hadith in which the Prophet, peace and blessings be upon him, says: “It is not permissible for a woman to travel a distance that takes a whole day and a night without a non-marriageable kin.”
the previous Hadith has many versions: in some occasions it says “a day and a night…” and others “three days.” Due to this, Imam Malik adopted the practice of `Abdullah Ibn `Umar, may Allah be pleased with him, in such cases. He used to shorten prayers within the limit of Reem (a place near Madinah) in a distance of four Burds (about20 km). Ibn `Umar, may Allah be pleased with him, used to emulate the Prophet, peace and blessings be upon him.
Most scholars understand the issue of shortening prayers as a form of dispensation or facilitation of matters, especially in journeys that involve hardship. As-Shafi’, Malik, and their followers, Al-Layth, Al-`Awzai`e, and scholars of Hadith like Ahmad, Ishaaq and others opine that a journey lasting a day is enough for one to shorten his prayers.
In his book Al-Mughni, Ibn Qudamah mentions that some scholars maintain that one can shorten prayers even in a journey of a distance less than the aforementioned limit (four Burds — about 20 km). But this opinion doesn’t carry much weight.
In the opinion of the famous four juristic schools, prayers are allowed to be shortened within a distance of 16 Farsaqs (one Farsaq equals three miles, and one mile equals 6000 arms length). So the distance here is about 80 km.
those who are excluded from this restriction in distance are the people of Makkah, Mina, Muzdalifah and Al-Muhassab. Whenever they leave their place of residence to `Arafat during the Pilgrimage, they are allowed to shorten prayers coming and going, as long as they are in the midst of Hajj rituals.
as for making the intention to delay the prayer, there is no need to voice it aloud, as this is related to heart. This rule regards all acts of worship save Hajj and `Umrah where one needs to make the intention for rituals audible.
there is a good example of the Prophet, peace and blessings be upon him, delaying a prayer, while travelling, so as to join it with the following prayer. He delayed the Zuhr prayer and combined it with the `Asr prayer. The same happened with the Maghrib and `Isha prayers, according to the Hadith narrated by Mu`adh Ibn Jabal, may Allah be pleased with him, which follows. “The Prophet, peace and blessings be upon him, in the expedition to Tabook, combined the Zuhr and `Asr prayers and Maghrib and `Isha prayers. When Mu`adh was asked why, he replied that the Prophet, peace and blessings be upon him, didn’t want things to be difficult for Muslims.”

As for your second question regarding the issue if it is permissible to pray full normal Prayer while travelling, we’d like to make it clear that Muslim scholars are not in agreement on this issue. But the most correct opinion is the view held by the majority of scholars that shortening the Prayer is better for a traveler, since the Prophet (peace and blessings be upon him) and the caliphs used to shorten their Prayers while traveling. This opinion, in addition, spares us the controversy whether shortening the Prayer is obligatory or not. However, a traveler is permitted either to shorten his Prayer or complete it, according to a group of scholars. Other scholars deem completing the Prayer while traveling as reprehensible since the traveler who completes the Prayer does not follow the Sunnah.

This debate is applicable if the traveler prays alone or is led by another traveler. If a traveler is led by a resident, then the preponderant opinion is that he should complete the Prayer.

To elaborate on the subject, we cite the scholars’ arguments in this regard:
In his book Al-Majmu`, Imam An-Nawawi says:

If the travel continues for three days, then the shortening is better. `Umran ibn Husain (may Allah be pleased with him) said, “I performed Hajj with Allah’s Messenger (peace and blessings be upon him), and he used to pray two rak`ahs. And I traveled with Abu Bakr and he used to pray two rak`ahs until he died.

Also, I traveled with `Umar and he used to pray two rak`ahs until he died. I traveled also with `Uthman. He used to perform two rak`ahs for six years, then he performed the whole Prayer in Mina.” Thus, to follow the footsteps of the Prophet is the better choice.

However, the traveler is permitted to complete the Prayer, as `A’ishah reported that she traveled with Allah’s Messenger (peace and blessings be upon him) in Ramadan to perform `Umrah. He did not fast but she did. He shortened the Prayer and she performed the whole Prayer. Then `A’ishah said, “O Messenger of Allah, you did not fast but I did, and you shortened your Prayer and I completed it.” He (peace and blessings be upon him) replied, “You did well, `A’ishah.”

In fact, shortening the Prayer is rukhsah (a legal concession) that can be abandoned, exactly as is the ruling of with wiping over leather socks in ablution.

Imam Ibn Taymiyyah says in his Collection of Fatwas:

Some scholars deem completing the Prayer in travel better than shortening it. Others prefer shortening but they see no harm in completing the Prayer. Rather, they consider it the apparent ruling and they say that one should not shorten his Prayer unless he intends to do so. Still others argue that completion is not permissible, and the Sunnah is to shorten the Prayer while traveling. According to them, it is reprehensible for a traveler to complete his Prayer. These scholars hold that shortening the Prayer is a permanent Sunnah for the traveler, while combining the Prayers (jam`) is a temporary legal concession. In fact, this opinion seems to be the closest one to Sunnah.

Shedding more light on the question, the Kuwaiti Encyclopedia of Fiqh states:

The Maliki, Shafi`i, and Hanbali scholars maintain that the original ruling is the completion of the Prayer, and the shortening is a legal concession. They corroborate their argument with the hadith narrated by Imam Muslim to the effect that shortening the Prayer is “an act of charity which Allah has given to you.” (Muslim, Abu Daud and Nasa’i)
Yet, the prevalent view in the Shafi`i School is that, in case a travel should last three days, shortening the Prayer is better than completion as it conforms to the Sunnah of the Prophet (peace and blessings be upon him), and spares us the controversy introduced by those maintaining the obligation of shortening the Prayer, such as Imam Abu Hanifah. In this context, some cases are exceptional, such as the crew of a ship accompanied by their families in their travels overseas, and one who is in permanent travel with no specific homeland. Such people are recommended to perform the whole Prayer to avoid the controversy introduced by a group of scholars, including Imam Ahmad, who hold that people in such cases should complete their Prayer.

On the other hand, the unpopular view in the Shafi`i School is that completing the Prayer is better in all circumstances, due to the fact that it is the original ruling and the oft-repeated practice. Yet if a travel would not last for three days, then completing the Prayer is deemed better since it is the original ruling.

Hanbalis maintain that shortening is better than completing the Prayer, as the Prophet (peace and blessings be upon him) and the caliphs always shortened the Prayer while traveling. Yet there is no harm in completing the Prayer for those originally allowed to shorten the Prayers.

Hanafis, on their part, have the view that qasr is the original ruling of the Prayer. Prayer was initially composed of only two rak`ahs for both travelers and residents. This is indicated by the hadith that `A’ishah narrated: “The Prayer was prescribed as two rak`ahs, both in journey and at the place of residence. The Prayer while traveling remained as it was (originally prescribed), but an addition was made in the Prayer (observed) at the place of residence.” As a matter of fact, this cannot be known except through tawqif (revelation). Thus, performing only two of the four rak`ahs by the traveler is not originally considered a kind of shortening (qasr). In fact, this is the original and complete ruling as far as the traveler is concerned. Also, completing the Prayer would not be deemed as rukhsah for a traveler, but rather an act of disobedience to the Sunnah.
Moreover, shortening the Prayer is `azimah (an established and confirmed ruling). Had the completion been the `azimah, the Prophet would not have persisted in abandoning it. It is known that `azimah is better than rukhsah, and the Prophet (peace and blessings be upon him) used to choose the best of deeds. He would abandon the better deeds once or twice only to teach his Ummah the legal concessions. He (peace and blessings be upon him) shortened his Prayer in Makkah and said to the Makkans, “Complete your Prayer.” If the completion of the Prayer had been permissible, he would not have performed only two rak`ahs.