I noticed some discoloration on some dishes I have. I assume this is from water seeping into the dish someway. Is there anything I can do to fix?
I can't comment on the first plate, since your photo is poor.
The second plate has a straight-up crack in it. Given that the crack is discolored at the edge and faint in the center, it's clearly spreading and will soon result in the plate splitting apart. Given the shape of the crack, it looks like a flaw in the plate itself rather than impact damage (from you hitting it on something), although I'd need to see the underside of the plate to be sure.
While there are ways to fix cracks in dining ware, none of them are great or attractive; it will always be obvious that this plate has been repaired. If other plates in the set are having problems, let me suggest that you'd be better off with a different set of plates. If all of the plates are cracking, they may have other things wrong with them that you can't see, such as using unsafe glazes.
Warning aside, if you want to repair it, the most effective method is to crack it the rest of the way in half, and then glue it back together using a food-safe epoxy.
Background: I'm a potter of 30 years experience.