Moen, Monticello Need help removing bath/shower cartridge

New to this board and to plumbing in general so any help would be great. I have a two stem (hot/cold) shower/bath faucet set up and I am unable to get the hot to shut all the way off - figuring it is the cartridge. I took off the handle and have provided pictures of the what everything looks like. Here are my questions:
1) Who manufactures my handles - there is no indications on the handles or the spout
2) Who manufactures the cartridge?
3) How do I get the cartridge out? If is stuck, what then?
4) I need to replace the handles/spout as well (broken internals on both), any recommendations that would fit the piping in the pictures?
5) How difficult is it to install new faucets?
Once again, I am stuck and would like to avoid paying someone to do this work if it is pretty straightforward.
Thanks,
Tim
Pictures:

Its a moen. The stems are held in by a plastic ring......(moen junk) they make a tool that inserts and you unscrew it. You can make a wrench for it also with some coppa pipe. Call Moen and they will have everything you need,including the handle rebuild kit and the wrench to install the new stems they will send you. I'm sure they will send you a spout also.

Thats a Monticello. Two handle tub and shower valve. polished brass and chrome.

Call 1-800-BUYMOEN and they will send you replacement parts IF you were the original owner of the faucet.