As flint92 already pointed out, "head" is a slang term used in Ireland, usually for a male acquaintance ("howya, head!"). Probably a shortened form of "head-the-ball", and equivalent to "skin" ("he's a dacent skin").
There is no obvious female equivalent, and it can't really be assumed that you would use "ceann" in the same way in Irish.
This exercise is "he goes out with a new one", not "he is going out with a new one". Even if téigh amach was used to refer to dating in Irish, It's unlikely that you would interpret the habitual present "he goes out" as a reference to dating.
This sentence simple means that he leaves the room or the building with a new one of something - a ball, a book, a bottle, whatever.