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Welcome to StackExhcange MABB. The Documentation of CiviCRM should provide all the information you need to set up a mailing subscription page: https://docs.civicrm.org/user/en/latest/email/set-up/.
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I would suggest you start by reading the section in the User Guide on Deduping and merging contacts if you haven't done so already.
As to identifying the contacts that need to be merged, this really depends on what information you have on record. Finding contacts with duplicate email addresses is often a good place to start. Or look for duplicate postal ...
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As far as I can tell from your screenshots, Groups is either (1) not installed or (2) not configured. Here's what you should see:
Note the extra column which shows the Groups groups.
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Just as you need edit_memberships to renew in the back-end out of the box, if you have Enable Access Control by Financial Type turned on you must then grant the corresponding financial types permission(s) that are used for your membership(s). e.g. edit_contributions_of_type_member_dues.
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