1- Yes, of course, if you need 1 point to reach the 8th star and you save 1 training point, the player have 7* but train like a player of 8*.
2- The cup, don't goes for Level, goes for Quality. So when is the day 1 of the season the game do the Cups depending of the Quality. The better 128 teams of the server in Quality terms, are in the called "Shark Cup" (well, called that here in the forum) and... the game do groups of 128. Some managers sell the better players at the end of season, to start the day 1 with less Quality and, of course, in a more easy Cup.
Don't belive that after day 3 one can have better season.... really don't know who... about day 3 of the season the only think I know is that, the day 3, start the league, and, is possible, to be in a league +1 level than you, so, if that happen, the day 3, you will have a scout list of 7 stars (some at 1 of Quality to 8*).
Thats why some managers that buy scouts wait for the 3rd day, because the list can change 6* to 7*...