Saying

Will you be my friend?

or

Can we make friends?

is not something that an adult says to make friendship. It only works after falling out with someone, when you already liked each other but had a disagreement. So it could be used to strengthen that liking, or to revive a broken friendship. In that case

Can we be friends?

might be a little better.

Saying

Will you be my friend?

or

Can we make friends?

is not something that an adult says to make friendship. It only works after falling out with someone, when you already liked each other but had a disagreement. So it could be used to strengthen that liking, or to revive a broken friendship. In such circumstances

Can we be friends?

might be better.