Flash video's don't use the video card at all, its 100% CPU dependent, so the intel graphics won't matter one bit. Yes, it'll run flash just fine.
That mini should be upgradeable to at least 2gb of RAM, not sure about 4gb though. But if all your father does is browse the web and watch online video's, then the 1gb should be sufficient.
That mini should be upgradeable to at least 2gb of RAM, not sure about 4gb though. But if all your father does is browse the web and watch online video's, then the 1gb should be sufficient.