My five year old does four hours of pre-team (level 2) and one hour of dance per week. She is happy and doesn't seem overwhelmed, but I imagine it's different for every child. We expect that she will begin to compete as a level 3 next September, at which point she will begin training 10 hours a week. That might be too much for her at 6. We will wait and see. If she needs another year of pre-team, then that's what we'll do.
Neither of my kids has ever had a private, although I considered scheduling one last year over a rogue front handspring with my oldest. I can't imagine doing them weekly. Especially for my five year old. What do they do in her private that they don't cover in her regular training? I don't mean to sound judge-y, I'm honestly curious! Do most kids in your gym do that?