Also, how did the poets use this kind of building and would it be too bold to assume that a temple of Apollo could have been there in buildings like this?
There is zero archaeological evidence of such a place. Piranesi was using his imagination, but there apparently was such an organization as a "guild of poets," variously called a schola poetarum or a collegium poetarum. It would not have been in the Campus Martius, probably, but instead either in the "temple of Apollo" on the palatine, in the sprawling complex started by Augustus, or else in a temple to Minerva on the Aventine. The evidence is very very sketchy and we can say nothing for sure.
The only definite evidence for the "guild" at all comes in Valerius Maximus (III.7.11), writing during the reign of the emperor Tiberius. He is looking back into the Republic, apparently back to 90 BCE, and writing about how a certain Accius remained seated when a certain Iulius Caesar entered the collegium poetarum. It seems that if there ever was such a place or an organization, it was earlier on and was disappearing or gone by the middle of the first century BCE. It might have possibly been related specifically to poets of drama. That it is basically never mentioned by the familiar poets of the Late Republic and Early Empire suggests that it either no longer existed or that they did not feel the need to belong to it. We have no idea what would have gone on inside a "guild of poets," but it would make a lot of sense as a sort of self-governed body of like-minded (or like-employed) persons, therefore identical to other, non-poetic collegia. The collegia themselves and Roman collective organizations in general remain very elusive to us, even the more well-known ones like the burial societies of the later Empire.
There is a bit of related material in Horace, in the 10th poem of the first book of Satires. It involves a person "Tarpa" who is possibly the "president" of such a guild. It is very convoluted and I won't go into it here; see the reference below for more. Martial is the one who talks about the schola poetarum, but we have no idea what that means, if it was an organization or a place or what, and whether it was the same or connected to the collegium or not.
For more, see Crowther, "The Collegium Poetarum at Rome : Fact and Conjecture," LATOMUS 32.3 (1973): 575-580.