There is still a big advantage of finishing third - teams automatically qualify for the group stages of the CL. If a team finishes fourth, they have to play a two-legged qualifier.
Not sure what the situation is with seeding either. When Leicester won the league, they were top seeds in their CL...
No, not for a while. Just this season there were five English teams in the Champions League after Man United won the Europa League last season (having finished 6th in the league). Spain had five teams in the CL the two seasons prior to that after Seville won the Europa League twice in a row...