Sure it can as long as it is dry. . Looks like a typical basement to me that people finish . Just remember the posts have to stay. Although some people will disagree. I prefer a drop ceiling over dry wall. It gives you easy access to the plumbing, electrical, etc when you need. Our present house has a dry wall ceiling and it is a PIA if we want to change or repair anything in the ceiling.

Thank you!

I depends on how high the ceilings are. Measure it to be sure and allow for ceiling tile brackets, etc.

You can use Fiberglass Ceiling Tile, they are flexible face and (vinyl and you can use them is I believe it is down to a 3" depth area.

I definitely think so! its a nice big space and often things can be moved or re-routed to clean up the space (not those beams tho) We redid our very basic basement and there were a few ducts that created a big headache - i thought it was going to be this big $$$ ordeal, our HVAC guy moved them for $800 - it was actually a pretty simple change (the lesson for me was don’t assume when i dont know 😅)