I was walking up stairs and I felt a pop in my foot. It is a little sore. Did a tendon slip out of place?

See a physician. If you felt a 'pop' and are having pain and swelling, you may have ruptured a tendon or a ligament and a thorough examination by a physician is needed to ensure you are treated appropriately.
Depends. Where did you feel the pop and did it prevent you from walking? Yes, a tendon can slip but it can also tear. Ice, wrap and elevate your foot. Something simple should resolve in a few days. If pain, swelling increases and you have difficulty bearing weight then get it checked. If it is improving start some simple motion exercises for your foot and advance your activity as tolerated.