This has nothing to do with the tense — the tense is decided by the conjugated verb. “Hanging” is an active participle (used in the “middle-voice”), while “hung” is a passive participle (implying that the paintings had bee hung by someone).Both have the same meaning, although “hanging” makes it sound like the paintings are “doing” something, while “hung” makes it sound like someone did something to the paintings. To me, the version with “hanging” seems most natural (in most contexts). Again, note that the tense is irrelevant — we could reverse them: 1 b.there is a painting hung on the wall. 2 b. I went into a room, with two paintings hanging on the walls. Note that “hanging / hung on the wall” is an example of a reduced relative clause.

I like Phil's answer. The words "hanging" or "hung" are superfluous in these sentences. You can say "there is a painting on the wall" "a room with two paintings on the wall". (better to use singular)

You can use hung which is past form or hanging which is the continuous form. There's no real difference for this context. There are many ways to phrase 1 sentence on English. I know this can be complicated.