How many hours after taking the pill do I wait before I can take other medication (such as rapid burn pills)?

Shouldn't matter. There should not be a problem with taking the birth control pill with over the counter medications or with almost any other prescription medication. Your best reference for this issue is likely to be your pharmacist.
It depends. Most prescription medications are safe to take with oral contraceptive pills but certain antibiotics as well as a few other medications can decrease the effectiveness of your ocp's. Your pharmacist can counsel you on this and it is a good idea to use backup contraception during the affected pill cycle just to be safe. Rapid burn pills are never safe to use.