Ok, I wasn't expecting a server-class card but it should be fine without its support bracket. Generic cases generally wouldn't have a place to connect the support to. (Some might, but I can't see the rest of the case. Your picture doesn't actually show how much space you have to insert a longer card.)

The dimensions of the P100 is 10.5 inches in length and 4.4 inches in height, so you should be able to measure for clearance. My 7900 XTX is 11.3in, and it will fit in many towers so I have confidence that the P100 will fit in yours.

Still, It's a long card so you might want to look around for a generic GPU support bracket to keep it from sagging over the long-term.

DIMMs (dual inline memory modules) are your ram sticks, yes. Typically, they run in pairs for best performance. So, generally, you would populate slot B and slot D for the first pair and slot A and C for the second pair. Regardless, the PC will generally still run with mismatched pairs, but it will clock itself down to the speed of the slowest module installed and may run in single-channel mode. This, in turn, slows the performance of the entire PC down by creating a bottleneck on the memory bus.

Edit: I haven't thought about slot height in a while, but standard cases are going to be full-height cards. Half-height cards are more niche.

Thank you for all your help remotelove you are awesome!! Here's a better shot of the space I'm working with. (Please dont yell at me about the dust its why I was heasitant to show I know how it looks lol)

I don't think space/length of cardwill be an issue. While I still have your attention I wanted to ask. In as simple an explanation as you can muster, what do I need to connect multiple GPUs to one motherboard? I don't quite understand how pcie lanes and bridges and all that work but from what I read its possible and you can use different manufactuer GPUs together for the case I'm doing. But how?? Theres only one slot. I know some boards have 2 or even 4 but theres homlabs with like 10 p100s chained together

Im going to clean the case. A few fingerprint smudges and a "smokeydope wuz here" drawn in should be enough dust removed

In all seriousness yep I plan to give it a real cleaning.