How could Fain possibly defeat a deity and become one himself?

The DO is a deity who is the equal of the Creator. A whole point of Jordan's universe seems to be that you can't get rid of Shai'tan permanently (he's outside the Pattern, remember). He's been there from the beginning and will be there to the end.

Fain has become a kind of walking manifestation of Mashadar. He's something like Shadar Logoth's Shaidar Haran (not literally, but thematically and all, it's what he is).

He's some kind of wilcard in the LB (one Rand can't take into account because he can predict Fain will be present at SG... if he turns out to be), but I think you exagerate his potential role.

Something more "reasonable" and in line with the role of Mashadar at the Cleansing may be for Fain to be used to force the DO to retreat briefly from the Bore, to lose his grip, to destroy the Bore. That would destroy Fain and whatever "part" of the DO is holding the Bore in place, but not Shai'tan. A big problem is that Rand would have to capture (and be able to hold) Fain before conceiving any such plan, and with Fain in the Blight already, that doesn't seem to be heading this way.

Another possibility, more in line with the "wildcard" aspect would be that Fain will deal with Shaidar Haran, a creature that is a limited physical manifestation of Shai'tan in the Pattern that Rand doesn't know about and won't take into account in his final plans unless he learns of its existence before going to SG. If Rand never learns of it and doesn't take it into account, Shaidar Haran could "ruin" everything by appearing at SG at the end, but based on the Cleansing where Mashadar and the Taint destroyed each other, it may be quite possible that a clash between Fain and SH would end in the destruction of both of them.