Will do. But let me clear one thing up: so, as long as my foreign drivers license isn't expired I can use it to drive in NY?
Correct. Your valid foreign driver license allows you to drive without a supervising driver.
And if my license is no longer valid and I only have a learner permit, I can't drive without restrictions anymore?
Exactly. NY State law requires a supervising driver to ride with you. The supervising driver must be age 21 or over and must have a valid driver license to operate the vehicle that you drive.