Yes, the ends of the plaster lathes are supposed to attatch to the beam but they are all burnt ends hanging in mid air. The beam looks weakened to me, like ¼ of the beam is burnt/gone? This beam supports the floor of the apartment above you? I'd say that part of their floor must be a bit spongy. You might be able to marry a length of 2x4 to the beam with long screws and catch the burnt ends of the lathes for their support. It will beef up the beam a bit and support the lathes. And it's quick and cheap, but not pretty.

Next time, you might wanna use multiple pictures upload (album) as a single post, to prevent from spreading comments over several related posts.

"Structurally safe" is a loaded statement/query. Timber framing systems are fairly resilient, and can stand a fair amount of creep, deflection, etc. before they fail. It's going to depend on what load is directly above, and how often loads cycle across it. has a good fix: sister a couple pieces of 2x4 onto the side of the scorched joist, push them up against the exposed subfloor ends to secure bearing and nail/bolt them to the existing joist. Add another sister to the opposing side just to make sure.

But definitely get the water issues taken care of first.

I'm sure there's a way to find out, but it will probably be a painful experience.

How old is it? Charring was a way to bugproof wood at one time, I think some still do it. Depends how deep the char is.

pretty bad picture, a video from different angle would be better

just looking at the picture, possibly there was something there that burned, maybe a filament lamp near the wood... or a jittery wire or a too thin wire

put a T support to be sure and have someone check it up

Looks like burnt wood to me, but the pic isnt great so no way to accurately tell for sure.

Even with an amazing pic... does charcoal scrap away from that black surface?