Will amoxicillin cure a bone infection from a root canal?

No guarantees... While root canal therapy most times does remove the source of the infection, there are times when antibiotics are used to remove any infection within the jaw bone. Amoxicillin may work. Penicillin may work. Clindamycin may work. Keflex may work. The decision on which antibiotic to use rests with your dentist and your medical history. We do the best we can but cannot guarantee amoxicillin.
No. Antibiotics control and help prevent spread of infection. Unless the cause of the infection is adequately addressed, the problem will return. In this case, if properly done rct and adequate antibiotic coverage, it's actually your own body that resolves the infection.