I completely rebuilt a staircase in my house because it had >2 inch difference in the rise between steps. It also had ~14 inch run per step so by dropping back to around 12 inch run I gained enough space to get the rise consistent and closer to 7 inches. Anyway, when I was ready to install pre-finished solid oak treads on my new stringers, I used a combination of construction adhesive and trim screws. You can find them at the big box stores. They make a small hole that I filled with colored wax. The hole is visible but not objectionable, at least to me. I installed screws only where the tread wanted to rock a bit on the stringers. If the tread sat on the stringers well, I just stayed off the staircase until the adhesive set up. The resulting staircase is solid.

I also cut a dado in the bottom of my risers and created a tongue on the back of the treads to fit into the dado. So the back of each tread is dado'd into the riser to help secure it.

With respect to a stair gauge I just measured for each tread. About half of mine are open on one side so they needed to be consistent in length and to be cut at an angle only if the tread wasn't square to the skirt board. My outside stringers are spaced by a flat 2x4 inside the wall studs so the skirt is just nailed up and the tread butted into it. In the closed part of the staircase, the walls were pretty parallel and I just had to cut the treads to length to fit. I would also say, however, that I think one of the reasons skirts and risers are often painted white - as mine are - is because it makes it easy to caulk small gaps. If you are also painting the skirts and risers, you don't need to worry as much about the tread fit to the skirts. As long as you cut reasonably well, any gap will disappear with a little caulk. If you care clear finishing skirts and risers, you will need to be more careful (or do what a previous carpenter did on another of my staircases and put up shoe molding to hid the gaps).