Do Bananas grow up or down from the tree?

A bit of both. Banana plants produce a flower which starts growing upwards from the centre of the plant and then bends over under its own weight.

The bananas emerge near the flower and grow upwards towards the sun. If the flower were returned to a straightened position the bananas would point down toward the ground (and then probably produce an odd twisted shape at it tried to grow toward the sun again).

http://www.tropicalpermaculture.com/growing-bananas.html (See under sub heading 'How do bananas grow?')