Glue Questions

Yes, you could use a paintbrush or simpler buy a glue that comes with brush in the cap like the Tamiya ones.

I use a variety of glues for modeling, each one has its application, good and bad points.
Plastic Cement/Glue (selection thereof)
White Glue
2-Part epoxy glue (different setting times)
Super-glue
etc

Some of those will work on a rnage of materials while others are specific.

Rather tha a brush, find a technical drafting pen which will allow much better control of placing liquid cements. If you must use a brush, get one with a pretty narrow point and use it only for glue. Acetone (finger nail polish remover) will clelan build up, but ultimately the brush will not last very long.