IOS – When using the Apple ID, how can I sign out from within an app

You can configure the VPN setting on your ipad, iphone or ipod touch to save the User Name and Password for VPN. I don't know of a way to have it constantly connect the VPN whenever the is a connection. Given the time it takes to establish a VPN handshake, it would be kind of frustrating to wake the device then not be able to connect to any internet/network related Apps for 15+ seconds while it connects to the VPN.

Choose Settings > General > Network > VPN > then choose the VPN Configuration. Fill in in the username a password section and then you can just turn the VPN on when you need it and not have to fill out the User Name and Password.

more info: http://support.apple.com/kb/ht1424

Alternative you could look at something like Apple's Mobile Access server, to give you that secured VPN like connection all the time without the hassle of starting a VPN connection:

http://www.apple.com/server/macosx/features/mobile-access.html

I was able to proxy URL requests from 4 apps I just tested (Instagram, App Store, Omni Focus, Bookmarks). I used a manual proxy configuration and Charles to test.

I'm not sure what proxy API you're talking about. From personal experience, I know that any app using an NSURLConnection to make the request will go through the proxy as defined by the system. It's possible some apps use a socket directly to make the request - if so that may bypass the system's proxy settings, but I'm not sure about that.