What is going on with my wiring!
The first way I tried to install was one black/black, one black/white
on the double wire box and capped the extra white and black
separately, and black/black and black/white on the single wire box.
This worked and the double fixture box turned on but the single wire
box did not.

The single wire box gets it's power from the double wire box, The second set of wires in the first box are going to the second box. (Power comes in on one set of wires and goes out on the other set of wires)
In the first box the blacks go together with the black from the light, joined  with a wire nut.
The whites  go together with the other black from the light, joined  with a wire nut. The bare ground wires go together with a wire nut.
Is there no green  ground wire on the fixtures? If there is they attach to the bare grounds in each box.
Since you are not dead yet, i will assume you know to turn off the breaker and TEST for power BEFORE you proceed