Some questions from a first PCB design attempt
First I'll answer your questions:


  How does the software decide the trace widths


I don't know. Read the fine manual. :) This is something you have to decide, not the program.


  I'm not using any surface mount components. Do I really need solder mask?


No, you don't. For the distances you have laid out, it looks perfectly solderable without a mask. But why do you ask? Every boardhouse will add a solder mask for free. If you're etching your own board, it's too much of a hassle to add one anyway.


  Do I need copper pour or ground plane?


Generally no, but you have to be a little careful with the routing of GND. Your layout isn't that bad, but you could have a more "starground" layout.

One thing that I would like you to do is to check carefully in the datasheet for your comparator if it's ok to leave the inputs open. It should be fine, but I'm not sure about this particular model.