Is it normal to shave private parts?

It's a matter of personal opinion.

Some people like to shave, some like to leave it alone, and some like to trim things. Any way you do it is up to you.

Some people like the way it looks trimmed or completely bald. Others like it to be hair.

Try it both ways and see which one you like.

It's fine and normal to shave if you want to, but natural is so much better. Looks better, and is more comfortable too.

Leave 'em alone. They look and feel better to both you and your partner.