Registration of new subscription

I am using the Membership plugin with GridMarket theme. I am also using the Login redirect plugin.
I would like to know the followings:

When users of my site go to register for a new subscription after they are done I get a message stating that they have completed registrations. After that my members have to naviatage to the login form and login to access anything. Is there a way to make it where they automatically login after the subscription is completed.

Using the GridMarket theme I have a custom menu in the sidebar. I am telling the membership plugin to not give access to the custom menu for free users. currently the plugin is hiding the custom menu options, but it is not hiding the title of the menu. Is there a way I can fix this?

Example: Free user

Menu Name > Members
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Example of login members

Menu Name > Members
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Manage your account
Renew or update membership

Is there a way to hide Menu Name> Member then the user is not login. I don't see the options in the membership plugin to hide the title of a custom menu