Use of deuxieme etage vs. premier etage; l'escalier vs. les escaliers

Question

Help - au secours s'il vous plait !
 
Instead of writing 'deuxieme etage', I wrote 'premier etage'.  I have always understood that the first floor, (which we Americans also call the ground floor), is the 'rez-de-chaussee', and what we in the U.S. call the second floor is 'le premier etage'. Collins dictionary defines 'second floor' as ' (US) le premier etage', which is what I wrote, and it was marked wrong.
I would appreciate an explanation as to the correct usage of 'rez-de-chaussee' vs. 'premier etage' vs.' deuxieme etage. 
Perhaps a hint as to the US vs British usage would be helpful in this exercise.
 
Also, when is it appropriate to use 'les escaliers' vs. 'l'escalier'? Collins lists them both as correct.
 
Merci beaucoup et bonne continuation !

Maarten Kamp · Accepted Answer

Hilary, 
I will leave the response to the point about a hint for the floor levels to the team. 
The story notes that they had already gone up a level by stairs though, and therefore could no longer be on ‘ rez-de-chaussée ‘. 
As they were talking about then going up to the next floor, one level further up, it could not be ‘ le premier ‘ or ‘ floor one ‘ in this context regardless of which naming convention is used.
 Larousse online covers the question of ‘ l’escalier ‘ or ‘ les escaliers ‘ as below. 
In short, both acceptable nowadays, with ‘ l’escalier ‘ more formal, although ‘ les escaliers ‘ is commonly used orally.
 “  EMPLOI
L'escalier / les escaliers. Dans la langue courante, en particulier à l'oral, on dit indifféremment l'escalier ou les escaliers pour désigner une suite unique de marches : monter les escaliers quatre à quatre ; la concierge est dans les escaliers ; descendre l'escalier.recommandation : Dans l'expression soignée, en particulier à l'écrit, préférer dans ce sens escalier au singulier : descendre l'escalier quatre à quatre ; la concierge est dans l'escalier  “. 
 On another point, I was a bit surprised to see ‘ panneaux avec l’histoire … ‘ accepted as the translation, but more surprised to see it noted as the ‘ best answer ‘. Not sure if ‘ panneaux sur l’histoire … ‘ is accepted at all as I just do the exercises without writing responses, but I think ‘ sur ‘ should be preferred over ‘ avec ‘ in this context.
I have confirmed this with my preferred free AI currently - Claude, and with my preferred natural intelligence French source as well ! 
https://www.toureiffel.paris/fr/actualites/visite/les-escaliers-decouvrez-la-tour-eiffel-autrement

Cécile Janty-Davies · Answer

N. Hilary,
To add to Maarten's answer, we have included a hint to clarify which floor is being referred to and to highlight the differences between British English and American English.
Maarten, we have also added  :
 
à propos de l'histoire ...
and
sur l'histoire ...
Bonne Continuation !