MobiControl and Secure Pulse VPN issues
For the first issue, are you using a certificate to authenticate to the VPN or the WiFi?
I remember a known issue with some Android devices where they will not open the certificate keystore until the end user has typed in a pin into the device. This can be problematic if you restart the device and the lock screen comes up. The device may not attempt to reconnect to the VPN until the lock screen is dismissed. This is a security feature in Android.
Based on your description I think the VPN is trying to pull the certificate before the screen is unlocked and probably is not smart enough to try again when it fails. An ADB log taken from the device may confirm this behaviour. If I am right then you may have to open a ticket with Secure Pulse. MobiControl just dumbly sets the configuration, Secure Pulse tries to make it work.