Do you mean the Vatican museums or St. Peters, or both?
With such a limited time in Rome, I'd skip the cooking lesson. I'm sure it's fun but do you really think you will learn things that you will apply to your home kitchen? At least I'd want to know which dishes they are going to teach you....no sense in spending an hour making pasta if you are not going to do that at home..
And I'd go to the market alone...do you know which one you want to visit?? Testaccio? What exactly d you want to do at a food market--snack? Learn about seasonal produce? (I'm not being sarcastic--I LOVE visiting markets--but do you really need a guide for that? I just wander around myself, ask a couple of questions if I want to learn something....always buy one or two items if a vendor takes the time to chat with me. Some markets have great, great stands where you can have lunch or snacks....like the one in Testaccio. There's also that huge market near the Vatican..Mercato Trionfale; I think it's the largest in Italy. It's not been packed with tourists when I have gone there.
Remember to go to food markets in the morning, or before lunch.
http://www.mercatoditestaccio.it
https://www.turismoroma.it/en/places/mercato-trionfale-local-market
https://www.througheternity.com/en/blog/rome-travel-guide/trionfale-market-rome.html
What kind of shopping will you plan to do?