Yes. Clone the delivered registration page, make your custom mods to the new one, and point your site to the new page through user.config, as documented in web.config:

    <!-- this key makes the Register link point to a custom registration page. leave blank to use the built in registration page.
    <add key="CustomRegistrationPage" value="/path/to/your/customregistration.aspx"/>
    Set RedirectRegistrationPageToCustomPage to true to force a redirect from the built in registration page to the custom url
    -->
    <add key="CustomRegistrationPage" value=""/>
    <add key="RedirectRegistrationPageToCustomPage" value="false"/>
 

No, you should not modify any mojoPortal code, you should avoid forking the code.

If you plugin your own custom registration page and you want to update your own table then you should create your own business/data classes for your custom table and store also the UserGuid or UserID to relate it to the mojoportal user. Then you retrieve both the SiteUser and your custom object based on the UserGuid or UserID and update your object separately.