If you need to add specific attribute to the MxAdmin user, you should create another entity linked to / inheriting of the user entity, not to account. All of your accounts are also “user” so it should work.
for your first question you may find interesting information here : https://docs.mendix.com/refguide/generalization-and-association
for your first question See Yehoshoua Choukroun’s answer.
For you second question, may I suggest to remove the administration module. That module is just not upto par. See https://forum.mendix.com/link/ideas/1569, please upvote. If need be, add module System management to have more grip on the entity useraccount, which only holds useraccount attributes but is confusingly named ‘user’.
To extend the System.User with attributes, add module Person, and in that module remove everything that you don’t need.