Well my solution to you is to go to the bios and switch the video from on-board/auto to PCI-E and/or go into device manager and disable your on-board video card. As an answer to question #2 the PCI 3.0 video cards are backward compatible with PCI 2.0 slots without performance loss.
Also have you installed the drivers for the HD 7770? I don't think a power supply can slow you computer down, it will either not turn on if there is not sufficient power. However you may have overheating issues, let us know your temperatures when playing minecraft with HWmonitor in the background.