Is it normal to fall in love with your best friend?

Falling in love with a friend does not happen for everyone, but it definitely can happen. Its certainly common for close friends to love one another in a platonic friendship way, but that does not mean that great friendships will always develop into romantic feelings or falling in love.

Is it possible to not fall in love with best friend?

There is nothing wrong with falling in love with friends, and in fact its quite common. The only thing you need to worry about is how you respond to those feelings.