Deleting Peoples App

Yes, not a good idea, you will lose everything. Maybe I am wrong, but I have the impression that there is confusion here. You cannot choose to display actions on your profile and not on others. Some actions are just hidden automatically like for example "Start conversation", "Messages" etc ... anything that you will not do with yourself is automatically hidden, you cannot choose that.
The only thing you can define is what is visible for each member level. There are two ways to do this.
The first: By prohibiting actions via the "Permissions" module. If you deactivate a function for the "standard" level for example, "Vote" then all the buttons relating to this function will disappear including on ALL the profiles belonging to the "Standard" level.
In this case it's not a question of seeing or not, it's more of a question ... of permissions.
The second: Via the "Navigations" module. There, it is really a question of seeing or not, but always only for each level of member.
I suggest that you preselect the "People" module so as to limit the number of menus that give you a problem.
Next to each item, you have the number of fields they contain, they should help you better understand the menu you want to adjust.
You are talking about the "More ...." menu, select this one. From there, either, you deactivate a section for EVERYONE, or you regulate it more finely by choosing the level or the levels of members who will be able to see it.

I hope I could help you, normally you should be able to put things in order, but forget about this idea of my profile and that of others.

I'm on UNA Cloud and the main issues I have are that certain buttons are either not working, appearing, or can be seen by everyone when they shouldn't be. Edit Person button is missing from Persons Actions but is in Persons More Actions. It's in View Actions also. Yet I can only see the button because I had to create it. The problem with that is now any user can see it on anyone's profile. It doesn't stay hidden....same thing with the module Customize... creating new levels won't help if I have no understanding how and why buttons are placed in Persons Actions and View Actions in the first place. If I can't toggle who can see what buttons on their own page versus others then interaction between Profile pages will become very limited. User (A) should not be able to look on User (B) profile page and see an Edit Person or Customize button. If the More button is enabled then why don't I see it showing? If I have submenus enabled why aren't they showing either? 

Sounds like Baloo is right your permissions are wrong.  Having others be able to see the Edit Profile button is good for Admin and Moderators.  Just go into permissions and set the which levels have that permission.  The Standard account should not.   

What's the difference between Account and Standard? I just want people to see Edit Profile on their own profile and not others. Don't know why it's set up so hard for people to have to toggle between multiple accounts to see who can see what. I have to have 3 tabs open. Admin to toggle buttons in Studio Navigation, a test profile to see what buttons appear on regular users profiles, and someone else's profile to see what buttons appear and disappear when my admin profile toggles the buttons on and off. It should be set up like this..

1.) Buttons you see looking at your own profile

2.) Buttons users see on other people's profiles

I have no clue what Profile Actions, Profile More Actions, View Actions, etc all mean in relation to what buttons show up where... to me Profile Actions means all the actions users can use and View Actions means all the buttons that have been enabled for users to see the buttons.... but half the buttons in View Actions don't even show up on profile pages.... so freaking confusing and it's been a week already getting nowhere

I am very sure you will lose all profiles if you reinstall the Person App. However, if you backup the database for Person App and reload after reinstallation it MAY work if done correctly, you need to ask UNA Team regarding this.

Meanwhile, all that controls what you see and don't see are under Permission n Navigation. Be sure you get familiar with them first.

Also note that you see Edit for other accounts when you are logged in as Administrator or Moderator, this doesn't mean standard user will equally see other's Edit link.

Well, the difference between "Account" and "Standard" is quite simply that "Account" is the step before creating a profile.
To give you an example, I have hidden as many things as possible so that someone who has created an account is encouraged to create their profile. A message is displayed explaining that no action is available until the profile is created.
DeDiary , I would not take this risk, too many things are crossed between the different tables of the base, it is a main module.
Will Roberts , like i told you, if it's ok with you i want to take a look at what's wrong, and then explain to you what your mistake is if there is one, but in my opinion it must be fixable , there is no reason.