For the battery setting, I would check that the profile has been copied to your computer and is not overridden locally. In the Advanced view of the BOINC Manager, select Options > Computing preferences... from the Action bar and check the setting in the Computing tab. If they don't match, you can select Use web prefs to delete the local preferences, or else update the local preferences manually, as is appropriate for your situation.

As to the GPU setting, it is designed to suspend GPU tasks while the computer is in use and to continue them once you stop. I believe it has no effect on anything else, including task fetching.

Just FYI, the Android client has a setting to compute on battery, up to an X% of drain, but understand the laptop makers don't use a standard API type function to allow this to be implemented for BOINC. My UPS can tell Windows to shutdown/hibernate though. Your Laptop might have such a functionality too in an orderly fashion, not just poof. That could hurt tasks in progress, particularly MIP1.