If one is prone to cheek/lip biting, what is the possibility of contracting an std (herpes, hpv) through sharing a cigarette with an infected person?

Zero risk: Nobody ever catches any STDs by sharing cigarettes or other oral exposures. Even kissing is no risk, except for oral herpes due to HSV1 (which isn't considered an STD) -- and even this is uncommon. Sores in your mouth make no difference at all. They call them "sexually transmitted" for good reason. Choose partners wisely and have safe sex -- that's all you need to do to avoid all STDs!

Not unlikely: Hpv is highly contagious. Risk depends on many factors, immune status.