The levels advance based on time. If you wish to advance them some other way, simply manually advance them (Ctrl+N by default). You can pause the clock, or set the time on each level to some very large amount so they have no hope of actually advancing due to time before you advance them manually.
You can restrict the number of rebuys and add-ons that a player can purchase, but there isn't a way to restrict a player to either 1 or the other. However, in version 2.2 (in beta test right now), the dialogs in which you purchase rebuys and add-ons display the number of rebuys and add-ons purchased by each player, making it at least a little easier to know whether or not a particular player is eligible to purchase a rebuy/add-on.