Friday is a day which Allah has made special for this ummah (nation), the nation of Muhammad (peace and blessings be upon him). It has a greater merit above all the other days of the week. There are a number of hadiths which speak of the virtue of this day, including the following:
It was narrated that Abu Hurayrah said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “We (Muslims) are the last (of the nations) but (we will be) the foremost on the Day of Resurrection, although the former nations were given their scriptures before us and we were given our after them. And this (Friday) is the day concerning which they disputed. So Allah guided us (to it), tomorrow (i.e., Saturday) is for the Jews and the day after (i.e., Sunday) is for the Christians.” (Narrated by al-Bukhari)
Al-Bukhari also narrated that the Messenger of Allah (peace and blessings be upon him) said: “The best day on which the sun rises is Friday. On this day Adam was created, on this day he entered Paradise and on this day he was expelled from it.” (Narrated by Muslim)
It was narrated that Tariq ibn Shihab said: “A Jewish man said to ‘Umar, ‘O Commander of the faithful, if this ayah – ‘This day, I have perfected your religion for you, completed My Favour upon you, and have chosen for you Islam as your religion’ [al-Ma’idah 5:3 – interpretation of the meaning] – had been revealed to us, we would have taken that day as an ‘Eid (festival).” ‘Umar said, “I know on which day this ayah was revealed; it was revealed on the Day of ‘Arafah, which was a Friday.” (Narrated by al-Bukhari, Al-I’tisam bi’l-Kitab wa’l-Sunnah, 6726).
In addition to what you have mentioned in your question, there are many acts of worship which are prescribed for the Muslim to do on this day. These include:
1 – Friday prayer
Allah says (interpretation of the meaning):
“O ye who believe! When the call is heard for the prayer of the day of congregation, haste unto remembrance of Allah and leave your trading. That is better for you if ye did but know.” (Al-Jumu`ah 62:9)
Ibn al-Qayyim (may Allah have mercy on him) said,
Friday prayer is one of the most important obligations in Islam, and one of the greatest gatherings of the Muslims. Gathering on Friday is more important and more obligatory than any other gathering apart from ‘Arafah. Whoever neglects it, Allah will place a seal on his heart.
It was narrated from Abul Ja`d al-Damari that the Prophet (peace and blessings of Allah be upon him) said: “Whoever neglects three Jumu`ahs, Allah will place a seal on his heart.” (Narrated by Abu Dawud)
2– Making a lot of du`a’
On this day there is a time in which Allah answers the du’a’.
It was narrated from Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) mentioned Friday and said: “On this day there is a time when no Muslim stands and prays, asking Allah for something, but Allah will grant him it” – and he gestured with his hands to indicate how short that time is. (Al-Bukhari and Muslim)
3– Sending a lot of blessings upon the Prophet (peace and blessings of Allah be upon him).
It was narrated from Aws ibn Aws that the Prophet (peace and blessings of Allah be upon him) said: “The best of your days is Friday. On that day Adam (peace be upon him) was created; on that day he died; on that day the Trumpet will be blown; and on that day all of creation will swoon. So send a great deal of blessings upon me, for your blessings will be shown to me.” They said, “O Messenger of Allah, how will our blessings upon you be shown to you when you have turned to dust?” He said, “Allah has forbidden the earth to consume the bodies of the Prophets, peace be upon them.” (Narrated by Abu Dawud)
along with these virtues and acts of worship, the Prophet (peace and blessings of Allah be upon him) forbade singling out Friday for fasting, or singling out the night of Friday for doing acts of worship that are not narrated in shari`ah.
It was narrated from Abu Hurayrah that the Prophet (peace and blessings of Allah be upon him) said: “Do not single out the night of Friday for qiyam al-layl, and do not single out the day of Friday for fasting, unless that is part of the habitual fasting of any one of you.”(Narrated by Muslim)