Actually this has been interesting for me as well
I would be worried about the current situation not least because there seems to be a loose heatsink. It obviously must have a heatsink or the processor would cut itself out every 5 minutes. I assume you know where the CPU is or you wouldn't have located it when it fell out. Is there a large chunk of metal attached to it with a fan on top?, there must be one there but does it wobble when you touch it? it should be rock solid when attached to the board and shouldn't in any way allow the CPU to fall out or even get hot enough to melt plastic. My CPU runs at a smooth 35 degrees C even under load although this is with watercooling. but still it shouldn't.
Your PSU must take 230V or it would have filled the room with smoke 20 seconds after you first turned it on but i am concerned about this situation as well.
This seems like a finely balanced situation. while nothing disturbs it, it works. But you are about to change components, and a large power hungry one at that. When PSUs die they can take out every single component they are connected to as well which is pretty much everything.
There is no need to get alarmed, but i would be cautious about what you do next. if you can please post pictures so we can advise on the best course of action