What exactly is the problem? Just because it says "offline" doesn't mean it won't be broadcasted. Anyway, this has nothing to do with mtgox, it's your client that's screwing things up.
Are you sure? Doesn't it mean if it is offline it is not in existent? it has been this way for 30 minutes.
no, every valid address "exists" (it might not belong to anyone (yet), but it's there). Try adding fallback nodes or checking upnp support to get more connections. Also, you're missing 1000 blocks or so. I don't know if transactions can be broadcasted before you have all blocks but you won't see any conformations until those are downloaded, that's for sure.