i've just finished my IR/CPL in Vancouver and Calgary after moving here from the UK so can't comment on the airlines, all i know is a lot more pilots move from Canada to the UK than vice versa! I'm about to start my instructor rating, and many of my peers back home are RHS on an A320 or 737 with the same experience! You won't get the ATPL here until you've got 1500 hrs, so i'd imagine you'd be best staying at Flybe a while longer to make the transition easier, or come and instruct on some 172s haha!
As far as the immigration works i have no idea, do what i did and marry a Canadian!
Many will moan about the crap pay and years it takes to a job, but it's a great country from what i've experienced in my year here, and i certainly won't be moving back to the Midlands anytime soon!!