I have ant. Left hip pain for one month that started one week after running a 5k (new runner). I'm limping. Advil (ibuprofen) 800mg doesn't help. What can it be?

Impingement. Could be a strain, sprain or impingement. You may benefit from physical therapy. Best to see your doctor for further evaluation.
Depends. Depends on where the hip pain is located. If in the groin, it is likely the hip joint and that would require rheumatologist or orthopedic evaluation. If low on the side of the pelvis, it could be bursitis.