No, my son does not do this. Could be "normal" could no be depending on frequency and type. Small toys in mouth are not usually normal at 4. Chewing on fingers or a shirt during certain activities could be. Just keep reminding her. My son used to like to pick his dry skin at karate. I made sure to moisturize and a couple months later (with reminding) he stopped.
I just saw your other post about your sensitive child...I suggest you look into Sensory Processing Disorder/Difficulties. What you describes sounds like Sensory Processing issues and I think it would really benefit her to see an Occupational Therapist.