Vacant days?

Does this mean at day 20 and 28 (no league or CL days) there are two matches in the League.

I like the idea, however I don't see the point of playing 7 group matches which do not matter much (these matches can be used to claim some negative achievements, since performing good in the group stage only results in a weaker opponent in the second round). Why not a tournament with many more teams, playing only one match each round (maybe with one or two group stages in it to generate more matches).
Maybe it would also be interesting to allow people ending third in a CL group to arrive in this new tournament (like in real CL/EL).

Does this mean that teams in the same league of year X will play against each other (and teams of a second league) in year X+1?

Still I voted yes, I like the general idea.