Well, that's colloquial, and colloquial wording is a bit of a slippery ground, we rather don't accept colloquialisms. But yes, that's a very basic one, it generally means "guy" and in such a sentence it does mean "I don't have a boyfriend/husband/partner".
They are Accusative form of "chłopiec" and "chłopak". They both mean "boy" ("chłopiec" is younger, "chłopak" is older, up to a young adult), but only "chłopak" means "boyfriend".