To answer your specific questions in order:
1. mintUpdate only asks for a password when you select it. This is not subject to change. A request to run any app that affects the basic structure of the OS will always require password input. This is a basic safety measure built in to the OS and cannot be changed (even if it could be changed it would not be a good idea).
If mint Update is asking for a password without you having activated it either from the menu or by clicking on the lock icon something is not right. Try going to Control Center=>Personal=>Startup Applications and removing the check mark for mintUpdate. This will keep mintUpdate from starting automatically on boot up. You will need to start it from the menu when you need it. Hopefully this will clear up the constant password requests
2. Wifi. If you are using encryption on your network, the request for a password may be coming from the encryption app. I can't help as I've never run or used an encrypted network. On an open network try right clicking on the wifi icon and selecting "Edit Connections". In "Wireless", click the line for the network you are connected to to highlight it then click "Edit". When the dialog box appears, make sure that the "Connect Automatically" box at the top is checked and the "Available to All Users" box at the bottom is checked. Click :Apply" and close the box and the editor.
Just checked something. Try this if your network is encrypted. Open "Edit Connections" and select your network as explained above. Click "Edit" and when the window opens, select the "Wireless Security" tab. Open the drop down menu labeled "Security", select the type of security system you use, and Fill in the boxes that pop up. Click "Apply" and exit the editor. This should provide your password automatically whenever you connect to the network.
3. Suspend and Hibernate recovery. Press "ALT + F2" to open the Run Program" box on your desktop. In the box provided, type "gconf-editor" (without quotes). Click "Run" in the lower right. When the editor comes up, open "apps" by clicking on the pointer. Scroll down to "gnome-power-manager" and open it. Open the folder labeled "lock". In the right hand window, remove the check marks after "Suspend" and "Hibernate". This will remove the screen lock when recovering from either function and thus remove the password request.
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