Yes, you can use any GPU. It will be almost necessary if you want to play new games or do something "intensive". For playing HD videos or relatively old games you'll be fine with the integrated GPU.
Being able to combine the power of the two cards is a desirable feature and is technically possible but it will depend on the motherboard and drivers, maybe the other graphic card and the application too. It is also important to be able to power down the stand alone GPU so power consumption is reduced when there isn't a lot of graphic work to do. You'll have to confirm this once you choose a model but it should be standard in every hardware above the low-end.