I picked up an old Kay K570 at a garage sale earlier today for like $30 because I thought it'd be fun to fix it up.

There were two things wrong with it that I have questions about: the nut fell off when I took off the strings, and it was obviously glued on. Should I glue it back on using regular wood glue or do I need something stronger?

The biggest question's about the bridge. The white part that's loose on the bridge, I think it's called the saddle(?), is broken on the end. Its adjustable, something that I havent seen on an acousitc before, and I want to know how much it would cost to get a new one. Id like to just get a new saddle if that's possible, I want to keep as much of the guitar original as possible. So yeah, if you can give me a rough estimate or give me a link to a website that would give me an idea, I'd really appreciate it.

Here have a waffle!
Couple drops of titebond for the nut, but as for the adjustable saddle... I'd say switch back to a fixed saddle. Gibson retired the adjustable saddle because the sustain was weak and the energy transfer to the body was very lacking. However, if you choose to stick with the adjustable, you can probably pick up a replacement saddle piece between $12 and $15 from the right people.
Just As I Am

MD PRS Style Semi-Hollow
Epiphone Les Paul Classic
Mesa Dual Rectifier
2x12 Celestion 30's
Kustom 200
8x10 EMC's
Yeah, I'd kind of rather have a fixed saddle, but the space for it on the bridge is a little longer than on most acoustics I've seen, and I'd really like to keep the original bridge, since I have no idea how to change it and I dont want to pay someone to do it for me.

I'll shop around and see what I can find. Thanks!
Here have a waffle!