Is the fast version or the slow version of "antager" in this sentence correct?
Version slow sounds more like "an tager" where fast version sounds like "an teger".
The normal speech sounds right to me. The TTS can be a little temperamental. In this case, the a has more of an /æ/ sound, and the g is soft, so it has a /j/ sort of sound. You can hear a real person's pronunciation here: http://ordnet.dk/ddo/ordbog?query=antage
(Copied from your other question, but with a different link. :)
yes and no.
it is called the "grammatical comma", in which you put a comma between a main clause and a following subordinate clause. but the "new comma" system, which is recommended, does not require a comma there before "at".
Both systems are accepted.