I assume you mean the transcontinental railroad? I don't think you're talking about this. Your picture is of the transcontinental railroad.

Unfortunately, I can't find any traffic data on the line from its early days. But I can answer the second part!

Rail lines don't need to have two tracks (one in each direction) to be useable in both directions. It helps, but isn't necessary. What can be done instead is a system of sidings that allow for one train to pass another, on a brief stretch of double-track. While this can slow things down (because the trains must wait for each other), it's capable of operating just fine in both directions without two tracks for the entire length.

Did they have places where a train could turn off from the main line and switch around?

Could you clarify what you're asking? Train cars are generally bidirectional, so you don't need to turn the whole thing. Locomotives in the US generally do have a particular direction they're designed to operate. They can be turned using a turntable or a track arrangement called a [wye](http://en.wikipedia.org/wiki/Wye_(rail)) or a balloon loop.