1. You will need to ensure that your PSU has a connector for the card - check the specs of both to be sure. There is a formual for deciding what power you need - certainly I have my doubts about 300 watts - but you first need to identify all the bits and pieces and add it all up - your monitor probably has its own power but, HDD, MOBO, CD WRITER, USB ports, CPU and so on. Frankly, you can get 550 watts quiet for under £30 so go for it.
2. The AGPx4 and the AGPx8 both have the same fitting so you should be ok, but that does not mean that your mobo will support AGPx8. Check your manual.