1. She invited me to her house and gave me a lot of food to eat. - This is fine grammatically. 2. She invited me to her house and entertained me with delicious food. - This gives a much better feeling about her hospitality, but 'entertained' is the wrong word when talking about food. Some good options would be: '...and treated me to lots of delicious food.' '...and spoiled me with lots of delicious food.' '...and made it a special occasion with lots of delicious food.' This is making me hungry! :)

Did she do something with foods while cooking or preparing them? "Entertain somebody with food" is uncommon phrase. The adjective "hospitable" is a appropriate word in this context.