Horizontal regression

All questions are a bit too general but could try some basic answers.
Regression tools purpose is to find the best true geometry through a set of points. The points can be COGO points or/and the result of the convert to centerline command (from 2 rails). The source doesn't change the way they are used.
You are the only one who knows what the maximum deviation must be. It depends on the project you are working on and the purpose of doing such regression. Also deviation is not the same if you are on a bridge or a crossing level where you may want to keep the existing track exactly at the same location to avoid having to do some work on the bridge or the crossing level. This is where you can set the point to "fixed" instead of the default weight (0.01).
There is no best method. Again it depends on the data you have to work with and what to achieve. Sometime quick regression can provide an interesting first set you can refine with other methods. Sometime using the curvature diagram with an element by element method is more interesting.
Slew diagram and sorted line are there to give a visual feedback on what you achieved.
Vertical regression is often more difficult to achieve because of large curves (R>10000) and small slopes. Difficult to choose between a curve and a straight.

All questions are a bit too general but could try some basic answers.
Regression tools purpose is to find the best true geometry through a set of points. The points can be COGO points or/and the result of the convert to centerline command (from 2 rails). The source doesn't change the way they are used.
You are the only one who knows what the maximum deviation must be. It depends on the project you are working on and the purpose of doing such regression. Also deviation is not the same if you are on a bridge or a crossing level where you may want to keep the existing track exactly at the same location to avoid having to do some work on the bridge or the crossing level. This is where you can set the point to "fixed" instead of the default weight (0.01).
There is no best method. Again it depends on the data you have to work with and what to achieve. Sometime quick regression can provide an interesting first set you can refine with other methods. Sometime using the curvature diagram with an element by element method is more interesting.
Slew diagram and sorted line are there to give a visual feedback on what you achieved.
Vertical regression is often more difficult to achieve because of large curves (R>10000) and small slopes. Difficult to choose between a curve and a straight.