You can change your email address at Settings > Account settings.
You will then receive a confirmation email on the new email address: please click the confirmation link in this email. If not, you will still receive all emails on the current email address. The confirmation is needed to ensure the new email address works: if the new email address is not correct, order notifications would not be received.
After your email address is changed you can log in with your new email address.
Your email address will never be shown in your shop: this is to prevent spam. Customers can contact you on the Contact page through a spam protected contact form.