Still have cheek swelling after treating a tooth abscess. Does that mean the infection had gone into the cheek?

Not necessarily. This may simply reflect the degree of inflammation surrounding the dental area involved. If however the cheek is red, tender, painful or if you develop fever, chills, etc., go back and see the dentist asap or your doctor.
Possibly. There coud still be infection in the area or liquis due to the surgery itself has accumulated. Possibly a problem with cellulitis. If it persists, seek the care of the doctor who removed the tooth initially. It could also be the wrong tooth was extracted!
Possibly. What do you mean by "treating? " Decay removal, root canal treatment, extraction, antibiotic coverage? Yes it is possible that infection has spread. Return to your Dentist for evaluation.