I just bought a low voltage track lighting system the other day, and I'm a
little confused.

1) The transformer box has 2 red wires, a black wire, a white wire, and a
green wire. The directions say to connect the black and white to the house
AC, and the red ones go to the track. However, the directions do not say
anything about the green wire. The directions do say though to cap the
ground wire from the house power supply as it will not be used. Do I need
to connect this green wire somewhere?

2) There is only 1 white and 1 black wire on the transformer, but where I
plan on installing it in the house there is a bedroom light fixture that
has 2 light bulbs (each with a black and white going to them). So would I
install this transformer?