tap+die sets are 30 bucks at harbor freight. you should be able to tap new, larger threads then use new screws.

>>951408
This is the pro way to do it without replacement.

Other wise nigger-rig it with JB weld

>>951441
jb weld holds fine but you normally yank on faucet parts so you must also mechanically secure it w/ bolts

>>951406
>My sink has been broken for awhile, it often pops out of it's mount because one of the screws in missing and the only other screw's mount is snapped. The one screw left is a bit stripped but even if I got it out there's not enough room to get in to screw it onto the other side.
your sink isn't broken, but your faucet is. the screws holding the spigot to the base are broken/missing. When those hoses flex enough they're gonna start leaking under the sink. You need a new faucet.

the good news is it looks like pretty modern faucet. modern faucets are easy to change.
it's the vintage faucets that can be a bitch to get out; they were made of solid steel and brass, and all the threads corrode together.

go buy a new faucet. You can put it in yourself, it's not difficult. There is two water lines to disconnect, and two big plastic nuts on the underside of the sink.

Protip: shut the water off, take your old faucet off and TAKE IT WITH YOU TO THE HARDWARE STORE when you shop for a new faucet. The nice hardware store people can help you avoid some common issues if they can see exactly what you are replacing.

Don't get the cheapest one there is, they leak and break a lot more often.
There's $30 ones and $300 ones. All the $30 ones are shit. Some of the $100 ones are shit. The $200 ones are generally good. The $300 ones are fancy designer jobs.
Save the box and receipt for warranty reasons.

Get one with a ceramic valve if you can. They're kinda expensive (~$200) but built better overall and the chances of leakage and breakage is much less.