about new players when we buy them,

Do they start at 15 and go to 16 when they do 30 days of buy  or when the season end ?

2 season=2month wait maybe xD

Your Youth Center is level 2 and can have up to 5 young players

why is it nerfed? last night 6 now 5 can you explain?

According with documentation:

1 season = 1 year 

Only promote to play with first team when the player reach 17 years. So u have wait 2 seasons, take patient uhg XD