Can't find a good glute strength exercise: I don't have enough grip/back strength to do high weight Deadlifts, My gym has no GHR machine, and I don't want to look extremely gay doing barbell hip thrusts (just kidding, my gym has limited space and is always packed, so I don't have the space to do them). Any other good glute exercises? I usually end up doing single leg hip thrusts with my shoulders and feet on benches (at my dorm)
Best glutes exercise out there is Bulgarian split squats. Next, i would say lunges and hip thrusts.
Is there a fast way to develop grip strength?
Grip strength training.
What are the best weight room exercises to stimulate arm pumping during sprints or jump windups?
I don't know, but you shouldn't do that in the weight room. Best way to get better arms efficiency at sprints and jumps = sprint and jump more.
Should I be trying to do my squats as fast as I can? I remember reading that faster squats translated to better vert gains.
No. You are doing squats to get stronger, so speed is irrelevant. Then you will want to express that bigger strength faster, so you will need to train RFD. Many ways to do that, one of them ( probably not the best though ) being fast squats. But you are at the first case now so don't bother.
Finally, a note: Your RDL is way too weak compared to your squat. Also RDL is not like full DL, you can bump the volume up a bit, don't ramp up to a heavy triple, keep doing sets in the 6-8 reps territory. But heavier than 135, 3x8 at 160-180-ish should be very doable for you. Start with ~160 and see how it goes.