Login without password

System Preferences --> Users and Groups --> Login Options --> Automatic Login --> Selected User you wish to log in automatically.

 

In System Preferences > Security > General, make sure you have UNchecked "Disable automatic login".

As for installing apps, you shouldn't try to disable password authentication. It's a security benefit, protecting you from giving an app elevated privileges without your permission. Since most users don't install apps continuously, it's not worth trying to circumvent this protection.

 

My wife doesn't like bothering with passwords. She never installs anything. So I set up her account for automatic login with no password. My account on her machine is the admin account and has a password.

I don't suggest an admin account with no password. I believe you can make your account auto login even if it has a password. But if you still want to make your account have no password, then there are a couple of steps I recommend...

1 - create a new user (you can call it admin if you like)
2 - make that user an admin
3 - give that user a password you easily can remember that's not something trivial like 12345 but not something painful like @HOUO*UE#KJLA- that you have to write on a sticky note which defeats the purpose of having a password in the first place.
4 - now that you have a "back up" admin user, make your account a standard (non admin) user and get rid of your password (if you like).

When you install things, you will get prompted for the admin user's account and password. Believe me it is worth it to keep around an admin account with a password so a visitor or passer by in the coffee shop can't wreak havoc on your mac without needing to know any password whatsoever.

 

Do you have this box checked? It's in System Preferences > Security > General:

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Do not find...

Do not find "--> Users and Groups --> Login Options". Where is that? It only says "Users" here and automatic log in is activated. Yet I am prompted for the password every time.