What if you take the birth control pill two hours late?

Answer 1

Only two hours - nothing. But don't start pushing it.
Yes, but in order for Birth Control to work at its best and prevent pregnancy, you should take it every day at the same time
This should not affect your fertility (or deliberate lack thereof) nor should it affect when your next period will start. However, if you are having sex you should probably use a back-up contraception (condom or other mechanical barrier) since the pill is 99% effective when used perfectly but is only 85% effective when used in the real world (due to forgetting pills, waking up late, etc.).
No not really taking it within 1 or 2 hours before or after your regular time should be fine. Some birth control pills have a stricter time frame though. Try to not take them anymore than 4 hours before or after your normal time.