Learn Italian: Mio nonno era molto generoso. - My grandfather was very generous.

In Italian, you usually need definite articles like il or la before possessives. However, singular family members are the big exception! Because nonno is a singular family member, it drops the article and is just Mio nonno.

Why use era instead of è stato for "was"?

era is the imperfect tense of essere (to be). We use the imperfect to describe a person's ongoing qualities and characteristics in the past. If you used the passato prossimo (è stato), it would sound like a specific, completed event rather than a description of his general personality.

Would molto change to molti if the sentence was about my grandparents?

No, because here molto means "very" and is acting as an adverb describing the adjective generoso. When molto means "very", it never changes its ending. It only changes endings when it means "many" and describes a noun.

How would I use the grammar from this lesson to say he was "more generous than rich"?

You would say Mio nonno era più generoso che ricco. Because you are comparing two adjectives (generoso and ricco) describing the exact same person, you use che instead of di for "than".