The present perfect tense expresses that. Adding "already" is accepted too.
Two things to note here. Were the subject a woman, the adjective would be "ženatá". Secondly, "ženatý" in particular does refer to being married to a woman (it derives from "žena"!). I believe the adjective for being married to a man is "vdaná" (or "vdaný" :)).
Correct. And so far the same applies to same sex marriage. Both guys are Ženatý, though that word actually comes from a word žena - woman and both women are vdaná. Easier here as that word originates from the word "Given".