This is tough, and its late so bear with me.

Honestly, jumping into something so soon won't be good for you.

If I were you, I would tell him you want to take things superslow and continue to be friends and be there for each other like you are now.

Getting over someone is hard enough as it is, and you are grieving for your grandmother which is a sad time as well. Just don't jump into anything is my advice. If he is truly your friend and wants to be with you, he will wait till youre ready. Nothing shows true colors more than patience.