I personally would tend to leave her if she's not actually upset - DD went through a stage of waking early but would eventually usually go back to sleep. I even worked out the "rule", that if she woke before 6am she'd go back to sleep, and if she woke after 6am she was awake for the day (my observation not what I enforced!) It's really good for them to be comfortable lying in their cot, and not necessarily a bad thing to be in there awake. Even now my DD will sometimes wake nearly an hour before "wake up" time and is happy to chat to herself without me needing to go in.
I have not at all answered you on the EASY/teeth/hunger questions I know sorry, because I don't have the answers; just wanted to reassure you it's not bad to leave her in the cot if she's not upset.