Will this cooperate with Windows 7?

Hello, Thank you for contacting us in regards to your question. 7th gen and newer Intel processors do not officially support Windows 7. Thank you, Newegg Support

does this product come with a stock cooler?

Mine didn't. But it also was not in the original packaging either. You would be better off with 3rd party cooler anyway. Hyper 212 evo is around 25 bucks and is good enough for mild overclocks.