Is the prayer of those being led outside the mosque valid, given that a staircase separates them from the mosque, and they are praying parallel to the rows inside?

There is no harm in praying outside the mosque if there is a need, and the prayer is valid in this case, even if a staircase or a barrier separates the worshiper from the Imam. The separation does not invalidate the prayer. This is permissible absolutely when there is a need.