The main thing that matter is the depth of the cabinet, not the drawer. Remove the drawer and measure the inside dimension of the cabinet, centered directly under where the opening for the drawer. This will tell you what size drawer slide you can use. It should be 20 or 22-1/2. The slide mechanism has some adjustability.
No, it is not recommended to be cut in shorter length
The drawer depth should be 1-1/4" less than the slide depth.
No it is a center mount
Mine measured as advertised - 22 5/8". I actually needed 21 3/4", so I used a hand saw to cut it down. So, if you need longer than 22 5/8", order the next size up and cut to length.
It was the full set, with rollers for the drawer and cabinet, back plate, and all screws.