Why is AMP asking for my Steam login details?
Some types of game servers on Steam can only be downloaded if the game they belong to has been purchased first. This is often the case if the server and the game are shipped as part of the same package.
In order to verify that have you have purchased the appropriate title, the Steam servers require authentication using a set of Steam login details as part of the download process.
You only need to do this the first time you use any Steam based game with a particular AMP installation.
Will AMP store my login details?
No, AMP uses the details once and then never stores them. The embedded Steam client provided by VALVe is responsible for storing a set of authentication details to avoid having to log in each time, but AMP does not do this itself. Your username and password are not stored or transmitted to any 3rd parties other than VALVe.
Why am I being asked for a Steam Guard code?
Just like when you log in from the Steam client on a new computer or in a browser, Steam asks to verify that your account is permitted to be used on that machine. So the Steam client AMP uses also needs a copy of your Steam Guard code to log you in for the first time. Like the login details AMP itself is not storing the details or sending them to anything other than Steam.