I have done none of these things, but have assembled 3 computers now for myself and a family member.
There is nothing about CPU cooler installation that is fragile, I am not sure that you could, even if you wanted, put enough pressure onto the CPU to damage it using your CPU cooler.
The only really fragile thing are the pins on the CPU which you can damage if you mishandle it. Being careful with it there is really nothing scary about it.
It's very possible to damage the socket and motherboard, if perhaps not the CPU itself. Those heatsinks and coolers are heavy, and they do also rely on pressure for proper thermal interfacing with the CPU heat spreader.
