Basic question: how wide is a "lane" on a racetrack?
 

I was curious as to whether this is standardized, like if all the gates have the same width, or whether it would be calculated by the width of the track divided by the maximum number of allowable starters (20 for Churchill, 14 for Pimlico, etc.)

The position of the gate varies from track to track. Some set it x feet from the rail, others set it y feet from the rail. I did a project once and found a starting gate company's website and used their dimensions for the width of a stall as the "lane width." However, it's not a Track and Field situation and horses can occupy more than one lane.

I believe the stall width was ~36 inches.