having the recovery partition is not a big issue. infact not an issue at all.
not having it is an issue if you need to access recovery to reset pc and stuff.
recommended to leave it as is. ~700mb anyway.
Is it now at least detected in the BIOS?
The error 3F0 (in HP) is because an OS wasn't found or its corrupted. Since you've replugged the drive, try the Windows install again since last time the issue was it didn't show the drive to install.
The BIOS update page and the CPU compatibility list pages are both not displaying anything, so we cant be exactly sure here.
Was the BIOS updated by you recently or at all?
You can of course try a 7700 to see if it does work. If it doesn't you'll have to find the BIOS update and update it.
Fan noises are usually not something that serious, and it can be due to a number of reasons. Since its a mechanical part, its prone to failure.
Most of the time, it touches the surrounding components or itself and makes sounds in the process, and perhaps turning it off and on moved it by a bit...
It's usually 2 pins that are close by to each other. I'd short out combinations to see if any works.
And no, i couldn't find pinouts. (do check the board thoroughly since it might have the pinout printed onto it somewhere near it)
Fan in the PS, GPU or the computer?
If only the GPU is being powered by the PS, you need to jump start the PSU first.
This can be done using a paperclip [guide] and is fairly simple. Once it's been done, you can power the GPU using a separate PS.
Were these new sticks put into the PC along with the previous sticks you had or do you only have these new sticks on the PC?
RAM stick getting abnormally hot is an issue, specially since its one specific stick. make sure XMP and other RAM OC are disabled and try again.
https://recoverit.wondershare.com/windows-tips/mbr2gpt.html
Here's a good guide on how to use MBR2GPT.
Before that though, try disabling CSM (compatibility support module) in your BIOS and see if that works. [if you encounter errors, turn it back on]
Have you tried resetting the BIOS by removing the CMOS battery to see if that helps? -- it could be because of a BIOS setting that prevent waking from input devices, so resetting might revert things and help.
Is your OS uptodate?
Do you have any pending BIOS updates?
Nope, there isn't a way for me to guarantee anything. You brick it, and you'll need a bios chip flasher or something like that to get the system working.
Even before that, you'll need a backup of the current BIOS as well.
Any unofficial BIOS you flash, idk if it will work, so its all up to...
so this started happening after they fixed the issue?
do you have mobile hotspot or another connection to see if the issue goes away?
are you on ethernet or wifi? if on ethernet, switch to wifi, and vice versa to see if that helps.