I took out my nuvaring yesterday and didn't get my period. This is only my first time taking it out. Should I be worried?

No worries. Everyone's different, it may take several days for your period to start, but if your period is delayed for a week or more, I would check a pregnancy test.
No. Cycle may be delayed sev days. It take an ave of 3 months to know your bodies rythm on a new birth control method.
Unsure. There is likely no medical problem in 1 day. If there is pain get checked.