The game itself almost certainly won't be a timed exclusive. PS4 sales are so much higher than Xbox One that Microsoft would have to pay a fortune to get timed exclusivity on the actual launch, and there's no way EA would alienate so many Playstation players. I can't see it happening in a million years after the backlash to Rise of the Tomb Raider and the clumsy, awkward and ridiculous way both the studio and Microsoft handled that announcement.
DLC is up in the air; Microsoft have been inking a lot of timed exclusivity (or "first on Xbox One") deals lately so I wouldn't rule it out. I hope not, but like you pointed out with Jaws of Hakkon, somebody at EA is clearly willing to do this sort of stuff.
I do not know; I would not put it past them. Rise of the Tomb Raider worries me because it could set a dangerous precedent for established, big name, hugely popular AAA titles going the exclusive route, or even the low, heinous timed exclusive route. I will freely admit that I am exceptionally bitter about the Rise of the Tomb Raider, this franchise being one I have followed avidly since Tomb Raider II (few people can understand how hard it is to be a hardcore fan of something if that something also includes "The Angel of Darkness"). Jaws of Hakkon did this as well and this practice BITES. I would hate to see yer another series I love go down that same route.
Although I suppose you are quite right in thinking EA would rather set a retirement home on fire before they would make Mass Effect an exclusive again. Unless they start hating money. In which case, this might mark the first time that blood sucking greed was actually considered a positive quality.