Probably just time for a new motherboard
Difficulty level 179274/10 wouldn't even attempt. Technically possible but odds are it won't work
Totally possible. You'd probably wanna get a robot to solder for you though as you're very likely to make a mistake.
Tiny Tom Logan did this a couple of years ago, he replaced all the slots on his board with different colour ones so all the colours matched or something silly like that. But I think he had it done by someone who knew their soldering. But it is possible.
I just had a look at an old MB to see. Desoldering and removing the old PCI-E connector would be very hard if you ask me. With clean holes and a new connector through the MB. I could see someone carefully soldering the pins. There very close together, would need good hands.
ive got one thats been desoldered for me, and id probably be taking to to an electronics store to do
theres a process similar to reballing that could repair it, Im not sure what its called but some hardware repairshops will fix it for you