You're intermixing multiple different (but overlapping) issues here.
First: Changing track widht on the fly.
While drawing a track, click on your mouse's right ear and select: "Select Track/Via width" from the popup menu.
If you make a list of pre-defined track widths in:
**Kicad / File / Board Setup / Design Rules / Tracks & Vias**
then you can loop through this list with "w" and [Shift + w] during laying of the tracks.
If you make tracks wider, and this wider track causes DRC violations, you can change this behavior with:
**Pcbnew / Route / Interactive Router / Settings**
If you set the mode to "Highlight Colisions" you can also "Allow DRC Violations**
Currently the interactive router has some problems with track segments of different widths. It is not able to move the point where the width changes. This is a known current limitation