It's possible, but given EA/Bioware's track record I doubt it'll be anything substantial. Just some cosmetic stuff.
I'm sure it's happening soon. The $10 expansion comes with NINETY days of playtime, and the expansion itself seems like it would cost more than $10 based on Bioware's standards of pricing on DLC.
F2P almost never really means the entire game goes free...they'll most likely limit character slots, inventory, which classes you can choose, things like that. It's more of a hybrid model that opens the game up to people who sometimes end up spending more than if they just subscribed monthly, while also keeping overall game activity healthy.
As far as I can tell they aren't going to charge for the first expansion, and the big update they've advertised for later this year isn't technically an expansion either way. If they do open up the hybrid model, that generally takes a lot of time to implement (I'd say 6-8 months after announcing it), so that likely wouldn't be until next year at some point.