In my opinion, you could check if he's treating all people like that or you specifically, to see whether he has feelings for you or is just a nice awkward guy. Either way, you can always tell him that you're uncomfortable with the way he compliments you and educate him on how to do better, though it seems unnecessary as long as it's harmless complimenting.

As for your boyfriend, if he's a good person in every other aspect, then it's not that he doesn't care, it's possible that he clearly trusts you and doesn't want to intervene with your place of work and relationships, which is a big positive.

All I am seeing here is a trusting boyfriend and an excessively friendly coworker. I think your coworker might harbour feelings for you or he might just like hanging out with you as a friend, but I'm kinda sure that he could be a little socially awkward. Even if he does have feelings for you, it doesn't matter as long as he doesn't act upon them.