Yes. Penicillin and Amoxicillin are in the same chemical family, along with all of the other antibiotics whose name ends in -cillin. People allergic to penicillin are almost certainly allergic to all members of this class, and should not be treated with any of the cillins.
Yes. Drug allergy evaluation. Like food allergy evaluation, requires a careful history and physical exam be performed. If needed skin testing can be done. Drug skin testing is very limited but there is guidance from the literature on most meds. It is important to remember that alot of drug allergy patients are mis diagnosed so a thorough eval is needed.