What is the name of these plastic bolt type things holding the PCB to the housing in the corner here?
Is there a way to remove them and then reattach them? I want to get at the PCB, modify it, and then reattach it, so that everything works as it did before.
They are called stand-offs and those are the kind that get melted almost like a kind of rivet. I'd suggest use a heatgun to soften them up while lifting on the edge with a pry tool.
Regarding PCB reattachment, if you want it neat looking, you can drill a small hole in the center of the removed stud and use a self-tapping screw to attach the PCB.
If the enclosure is providing electrical isolation, make sure not to accidentally drill all the way through, and don't use too long screws.
These stand-offs are melted to hold the PCB, as DanZ has said. Instead of softening them, I usually prefer breaking off the flattened part of the plastic stand-off and the using gluing the PCB there (using hot glue if I plan further modifications and I do not need any significant strength) or melting a fresh piece of plastic (scrap or 3D printing filament) to hold the PCB. When the second variant is performed properly, you can get reasonable strength and PCB mounted there by the exactly same method as the manufacturer has used.
Might also be called a "boss"
https://en.wikipedia.org/wiki/Boss_(engineering)
The type of standoffs/rivet where a plastic peg is melted at the top to form a permanent fixing is called a 'heat stake', e.g. https://www.amadaweldtech.eu/applications/electronic-components/heat-staking-pcbs
It may also be just a push pin. Prying up may pop it out.
