Do I have to replace this entire valve or can it be fixed?
This is definitely a Moen shower valve, with a common Moen cartridge. There is no "seat" per se. You can perform a simple replacement of the cartridge and it should solve your problem. First you need to shut off the hot and cold water supply.

If you look closely, there is a horseshoe shaped retaining clip with a small hole at the top of the inverted "U", this holds the cartridge in. Once the clip is removed, there are various ways (all involve pulling) to remove the old cartridge, my favorite being using a stiff steel bar with a hole in it, screwing it to the protruding stem, and using the handle/knob screw to fasten the bar to the stem as a "pull handle". Then I twist and pull to remove the cartridge. There are brass (old) and plastic (new) cartridges, they are interchangeable.

There are various other ways to assist in cartridge removal, including a special puller tool manufactured for that purpose. You may be able to borrow or rent the puller from a good plumbing or hardware shop. There are circumstances where the puller tool is pretty much the only tool that will work.

Replacement is simple, insert the new cartridge and install the retainer clip... done! Moen guarantees them for life too, so if you send them back the old one they will send you a new one free, for next time.

 
 

Check out this video