Questions on quarterly estimated taxes

I'm a freelance art director in NYC and have a few questions:

1. I didn't realize we had to pay estimated taxes by certain dates for each quarter, so haven't paid taxes on income I earned earlier this year. I'm planning on making payment by September 15th for all income I earned so far. Will that be ok? or will there be penalty for not making deadlines for each quarter (will they even find out in which months/quarter I received payments from my clients??)

2. Do I need to pay state tax as well?

3. Can Turbotax figure out what I owe??

 

Thank you!