Soldiers are ordered to shoot with the scorpions by the command "Fire!". It does not make sense to use the word in a fictional world, where combustion weapons are not invented. The command for bow-type weapons would be "Loose!".
Arya and the Hound left Winterfell in the previous episode Game of Thrones: The Last of the Starks before the Northern army. They are supposed to travel much faster (as opposed to army with thousand of soldiers and provisions, etc.) and they have no motivation to linger anywhere. Yet they arrive after the Northern army reached King's Landing, and even after longer time when they established siege perimeter.