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I can’t help much on the power draw side of this question, but one thing to look out for with a UPS is some sort of communication option. (Usually NUT over ethernet, but there are some USB options too.) Most modern UPS brands will have a plugin you can install on your Raspberry Pi and Mini PC that allows your UPS to signal, “Hey, I’ve got 3% of battery life, you actually need to gracefully shut down now.” It’s mostly useful for NAS applications with spinning drives, but it could help save your Pi’s SD card potentially.
It’s a pretty standard feature these days, but the cheapest of the cheap will omit it.
This is pretty typical for universities. They don’t want the airwaves clogged, doubling up NAT can lead to networking wonkiness, and they don’t want you giving university network access to unauthorized folks with an open AP.
When you say VR streaming, you just mean wireless from your PC to the headset, right? There’s a chance you could do that with an offline wireless router if the VR experiences you’re looking to play are single player.