No to both. Zapdos can be found post-game (which means beating the Elite Four) roaming the region only if you chose Fennekin. If you chose Froakie you'll get Moltres.
If you chose Fennekin and see Zapdos 12 times in the region, it'll appear for battle at the Sea Spirit's Den. The same goes for those who chose Froakie except it'll be Moltres.
So yeah, if you chose Froakie you'll have to trade for Zapdos.