Installing Hikashop Essential

If I install hikashop essential will it erase all that I've done with hikashop starter?

No. You won't loose anything.

I've installed HikaShop Essential and turned off the registrations and login features but the registration fields are still showing. How can I fix this issue?

Could you give a link to your shop so that we can see it ?
If you're talking about the email address field and the address fields, that's something else. It's normal. The email address is necessary so that HikaShop can send the emails to the user and the address fields can be tweaked via the menu Display->Custom fields. If you really don't want to ask any address information and the email, you can remove the view login_ and address_ from the "checkout workflow" option of the tab checkout of the configuration.