I believe wonen means residing somewhere, not actually living. I think the confusion comes from the double-meaning of the word "living" in English. Sometimes living actually means something is alive, but sometimes it means someone resides in a place, as in "this is where I live". Dutch and German seem to have two different words for the two distinct meanings.
leeftijd means age. Well, you can also look at it literally -- leeftijd is the time you've spent living so far... Very literal, the Dutch. :p
It means basically the same, but the difference is that "alive" is an adjective. Using "living" more directly translates this "leeft" because it maintains the verb-function on the word.
That's a perfectly fine translation of "leeft het"
Though unrelated to what you are replying to here :)