A stall is a small partitioned area and a toilet in in a partition so it's called a bathroom or restroom stall.
The term restroom came from the fact that in early 1900s up-scale restaurants, theaters and performing facilities would often have comfortable chairs or sofas located within or in a room directly adjacent to the actual toilet and sink facilities.
The reason public toilet seats have a gap at the front is to allow women to wipe their perineal area after they use the toilet without contacting the seat.
Basically the gap in the toilet seats is there as required by code and is there to help people clean up better after using the toilet.
The capital city that has the most public toilets is Madison Wisconsin.
Madison, WI, is the US city with the most toilets per 100k.
The country with the highest density of public bathrooms is Iceland: 56 toilets per 100,000 population.
Wakefield is the UK city with the most restrooms per 100,000 people (35) and per 100km2 (130).
Berkshire, Merseyside, and Greater Manchester are tied as the counties with the fewest toilets per 100k population (three).
Madison, WI, is the US city with the most toilets per 100k (35).