Did she cheat on him?

Now, I felt like this was a loose thread and was pretty confused when later in the show they were shown together without resolving this issue.

It's not clear whether there was erm... physical intimacy between Debbie and the classmate but there was certainly "cheating" in some form.

It's clear that there is an attraction between the two and closeness [look where his hand is] ... and certainly she doesn't seem to mind the closeness and it looked like she felt guilt when they were caught.

Months later...we see Ford walking past the laundromat and he sees Debbie inside.

The interaction between the two indicates, at least to me, that even if she did cheat he elected to forgive her and rekindle the relationship.

So the "resolution" was unspoken and, for the most part, unseen but that's not to say it won't come up again in Season 2.