Sheikh Attiyyah Saqr – may Allah have mercy on him- said:
One way that Allah SWA made the Muslim Ummah special, is that He made all the earth a mosque, thus, wherever a person finds himself when it is the time for prayer, he prays, and as long as the earth is designated by Allah SWA for the prayer, and people pray on it, it becomes a mosque, and it has the rulings for every mosque. The prayer there becomes better than the prayer in any random area of the earth. Mosques themselves have differences in term of superiority and preference, and the best of mosques is Masjid Al Haram, because the prayer there is worth a hundred thousand prayers in another mosques, followed by the Masjid in Madinah (Masjid An Nabawi) because the prayer there is worth one thousand prayers, then Masjid Al Aqsa because the prayer there is worth five hundred prayers, and there are hadiths about all of this.
As for the rest of the mosques they are equal in terms of reward, and some of the scholars have said that the bigger mosques are better than the smaller mosques for prayer, and some other have said: the mosque that is further away is first, due to the number of steps it takes to get to it, and it is all a matter of preference.
As for prayers performed in any mosque, it is a valid prayer there is no doubt about it. Congregational prayers can also hold in it, Friday sermons, and Eid and other events according to the majority opinion that sees all the masjids as same in terms of holding Friday prayer. As for this there is no difference between old and new mosques.
If the owner of the building wishes to pull it down, the mosque would still remain a property of Allah SWA, and it is built anew and is not destroyed nor is it used for anything other than prayer.