Women smokers who take birth control pills have an increase risk of stroke, deep vein thrombosis and narrowing blood vessels. Birth control pills aren't recommended for women over age 35 who smoke because it increases the risk of cardiovascular disease. If you're 35 or older, and you smoke, you need to quit smoking before you can safely continue using your birth control pill.

I'm still in my 20's so it's still relatively okay to smoke while on the Pill? It does not affect the Pill's effectiveness at all in any way? And is it still safe to have sex during the 7-day break off the Pill (breakthrough period)? Thanks!

It's never "safe" to smoke while taking birth control pills. It really isn't "safe" to smoke, period.
My sister's doctor (we share the same doc) told her that she needed to quit smoking because of the risk of heart trouble/stroke. He recommended that she get fitted for a paragard IUD. She has never been pregnant either.

Just because you asked, smoking does not affect the pill's effectiveness in any way, shape or form.

Also, it is safe to have sex during the 7 day break off the pill. You're still protected. The break is to make your body have a period. If your pill doesn't make ovulation quit, you most likely would have already ovulated during that cycle. Ovulation occurs before menstruation, so you're safe.