The cup competition always has teams of various levels, just like real life.
As regards the league situation, playing in a higher league level than your own managerial level, comes about when there are not enough of the higher level teams to make a complete league and so they have to make up the numbers with teams from the next level down. Hence you have higher level teams in your league. It is a pain, but the upside is that ALL of the players on your scout list will be 7* players instead of the usual 6*.
I am in your same position this season, level 15, playing in level 16 league.