Can POP (Plaster of Paris) and Paint done without waiting

I don't think sanding the surface will produce a surface good enough to paint. It's certainly a lot of effort for uncertain results.

If the underlying surface is very rough it might still show through the wall paper, unless it's very thick (1000 gsm lining paper for example) or you do some sanding.

The best answer might be to continue to peel off the paper and then skim the wall with plaster. Depending on your plastering skills you might want to get a professional in.

The result should be good enough to paint.

You won't have luck applying paint/stain to a soaking wet deck. If there are common walkway areas on the deck you could put down strips of grip tape along this route. This is tape that has a sandpaper texture to it and is meant for slippery decks and stairs. Maybe not ideal, but a solution until you can properly treat it.