My 3mo enjoys putting her fist in her mouth and chewing on her thumb. Is this part of her motor skills development, and should I pull her hand out from the mouth whenever I see her doing that? Sometimes, she will suck her fingers till she vomit as well. ?

It's part of exploring their hands and fingers. I tried to pull it out and warn baby and even smack baby it it didn't work - maybe I didn't persist Long enough. My boy is 6 months now and he still does it. Waiting for him to out grow it. You can reduce it by giving them pacifier or other toys or soothers to chew on. My boy loves a chilled tether and a hard metal ring - so u can see for yourself how u wana handle it. Some people feel better to use soother for fear of next time hard to quit sucking hands and easier to quit soother (just don't give)