at this point in time, is keith with the guy or is he single?

Their relationship occurs at the same time especially later on this chapter Yeonwoo who's preggo and josh will meet in the party if you remember that scene,so we will meet yeonwoo and kieth in this style xD

I think, at this point, Keith and YW might be in their first phase of dating, where they're being cute. If not that, then they're undergoing their first breakup currently. In a couple of chapters (the timing is confusing it could be a few days or a few weeks) Keith holds his big movie party where Josh and YW meet for the first time and Keith is all pissy because he'd been marked but didn't know who did it yet.

Well the knife incident happened shortly before this assignment, so I'd say it's when YeonWoo is having lunch with Emma and Keith is getting desperate.