If I get a penalty from New York State, can I pay it and the withholding all at once?
For example, my withholding tax in NYS is $1k, and my penalty is also $1k. Can I can pay all $2k at the same time?
I'm not sure what you mean by "withholding tax" but typically you pay any penalties when you file your annual tax return; it is added on to your total tax amount and used to calculate your net tax due or refund.
For example, if you have $10,000 in income tax due, have a $1,000 penalty and had $10,500 withheld throughout the year, when you file your state taxes you'll have a net tax due of $500 (10,000 + 1,000 - 10,500).
If you're asking if you can pay the penalty earlier - such as with an estimated tax payment, then sure - it will just count as taxes already paid when you file your annual return.