But the delay in processing really affects a lot. Can I train rookies now with Friday’s update? do my player’ minutes from last season also count? Is a 23 year old going to be trained as a 23 year old or 24 rate?
Yes you can train with Friday's update.
Yes minutes from last season also count -- as you can see from the Weekly Stats page (click on your team's name in the Menu, then in the drop down in the top/right of the main portion of the page, choose Weekly Stats).
Yes your player will be trained at his post-update age (rookies won't update with the age update).