Can you fit a low profile graphics card in it? For example, a NVIDIA 720 or 1030?

It is not a low profile case so it won't work unless you can find a normal bracket for it. A lot of manufacturers supply both when you purchase the video card.

How many 3.5 inch internal/external bays?

There are 6 internal 3.5" bays: 4 in the included drive cage, and one more vertically below the drive cage using the included rails. There is one more 5.25" to 3.5" converted included in the top external 5.25 bay.