¿Cuál es la diferencia entre amar y querer ?Puedes dar oraciones como ejemplo.

As it has been already said we use "Amar" with family, friends and all the people we love deeply.
"Querer" is both an expression of desire, you can want something material like in "quiero comprar una casa", "quiero un helado", "¿Quieres un helado?", but it also express affection. You definitely say "te quiero" to your family and friends, just like in "te amo", but the feeling, the intention behind the word "amar" is stronger.
The sentences "mi abuela me ama", "mi abuela me quiere", are correct, both of them. It would depend on what you want to convey. For example, I don't say "te amo" to my friends and my mom all the time, I say "te quiero", but when I am in a trip or I want to convey this deep feeling of love I say "te amo". But, that might depend on each person.