Register new user in the frontend

Yes, yes you can.

The relevant functions to do this are:

• wp_create_user Creates a user given a user/pass/email
• wp_insert_user Creates or updates a user given user/pass/email
• add_user_meta Adds User Meta ( same as Post Meta/Custom fields but for users rather than posts )

You’ll find examples on how to use those functions, and links to more possibly relevant functions. Use these functions in your form handling code on submission, make sure to escape all values entered.