Following the trail back in time, Progress Rocket Space Centre -> TsSKB-Progress -> Progress plant, named by the Ministry of General Machine-building in 1965.
As that's before the spacecraft (programme initiated in 1973), the centre is at least not named after it.
Though the word "progress" is pretty generic, both the plant and the program ...
What would happen if there was a freak accident in which that the ISS needed to be evacuated and there was ONLY one space craft available?
Carrying that to an even greater extreme, what would happen if there was a freak accident in which the ISS needed to be evacuated and no space craft was available? For example, suppose two human-qualified vehicles are ...
By design that will never happen. There are always enough return seats for the crew.
This is exactly why
the whole crew of one of the visiting vehicles gets in it whenever it undocks, even when it is only being moved from one docking port of the station to another
the crews retreat to their vehicles in fire / leak / toxic atmosphere emergencies
the crews ...