If you have no master password set, then the login passwords are always available. If you do have a master password set, then opening the Saved Logins dialog will prompt you for the master password. Without the correct master password, the list of logins will be empty and thus there is no password to copy.
The bug only occurs in this specific condition:
Integrity is what you are looking for. With integrity, the receiver can check that the message is valid. One can use Message Authentication Codes like EAX and GCM. Take care of the order of operations if you insist on this. Also, take care of proper padding if you are using RSA. For encryption PKCS#1.5 and RSA-OAEP and for signature RSA-PSS.
Normally, we ...
The same as using plaintext (unencrypted and unauthenticated) communication elsewhere.
What exactly that means, depends on your threat model.
Smart Bulb, Dumb Protocol
Imagine you had a smart lightbulb in your home. You could use an app to control the brightness and the warmth of the bulb. It even offers an API, so you can control it via a Raspberry Pi ...
No, it cannot
There is no such mechanism in RSA.
Even if you have the private key you can't check if a message was encrypted using the corresponding public key unless you know something about the plaintext (for example, that is should be readable ascii and not random bytes).
If you implement message authentication (i.e., the message is also signed using ...
Just use stronger encryption.
I don't think that a locked home with a safe in it is a good analogy for double encryption.
The security on most homes is similar to the security that rot13(*) provides: It keeps honest people honest, but a brick through a window or boot to a door provides access.
Double encrypting would be like ...