1. When a piece of equipment becomes damaged... room is completely useless thenceforth? Tried every combination and manner of clicks to "clear" damaged equipment to no avail.

2. When some staff become dead tired, I pick them up and place them into break room... then the room they were in becomes completely uninhabitable by any other staff. Tried placing all manner of folks back in room, and the staff are still greyed out - none of the non-occupied staff will automatically go in there and treat patients either - whom still queue outside room as if waiting for staff. They just get frustrated and leave or die. Actually had a break room go "useless" as well - completely empty, and no staff would venture in there - when manually dropping them, they're greyed out and not able to be dropped.

What's the dealio?

I don't remember how it was with your second question. As for the first: I'm fairly certain you cannot clean this room. I guess it's a punishment for letting it happens. Pretty silly, yeah, but that's how it is.

With the second question... I've had a glitch at one point where picking up a doctor from the operating theater glitched it out (one tile of the theater became a clone of whichever tile he inhabited from there on), though I think that was a different bug. Maybe try tweaking your hospital policy so that they will automatically go to the break room when they are slightly less tired?

The first one is an easy answer, though: When a machine explodes, it renders that area completely unusable. You can't use that room, and you can't build anything else on top of it; it's just gone. The solution: Get thee a skilled handyman, and switch his priorities to only fix machines. Keep an eye on how much they're being used and replace if they are becoming worn down, and research upgrades so that they become more durable.
If a machine starts smoking (heaven forbid), it's possibly better to replace it than risk it being used any more - and when the earthquake warning sounds, pause and check all your machines - ones that are already damaged will take a heavy hit from an earthquake.