What is the SOL for credit card debt in New York? How do I find out if SOL has run out on a debt? Do the collection agencies or law firms have to supply proof that SOL has not run out?

http://www.cardreport.com/laws/statute-of-limitations.html

For NY, it's 6 years.

... but beware: the SOL is based on the date of last activity, which includes affirmation of the debt, payment made, charge to the account... whichever is last.

What does date of last activity mean? Affirmation of the debt... does that mean acknowledgement that is by phone or writing or by not responding to a collection letter?

Certainly a letter to the creditor or a phone call discussing the debt could be acknowledgment. Primarily, though, what sticks folks is the last payment issue:
Folk want to do the right thing and make a payment... but that sets the clock back another x years.