To reduce the confusion with the geometric meaning of square I suggest adding an additional on hover translation of 'town square' for náměstí. Town square is what is meant when the shortened version 'square' is used in English. 'The big square' without context in English would suggest primarily the geometric meaning.
Yep, there is no "a" or "the" in Czech, but when you would say "THE big square" it would suggest that you are talking about some specific square you mentioned earlier in the context probably. In Czech, that could be expressed as "TO velké náměstí", where TO is literally like a word expression for pointing at something specific. Example: "Which square do you mean? THE big square in the center?" "Které náměstí myslíš? TO velké náměstí v centru?"
It is true that Czech does not use articles like the English "a" and "the." So it puts demonstrative pronouns to use for that purpose.
The course consistently uses "ten" (in its various genders and cases) as EITHER "the" or "that." Sometimes in our translations we can pick one or the other based on context. When there is no context -- which is most of the time... -- either one seems to be accepted.
"Ten (etc.)" is never translated here (anywhere?) as "this." "This" could be either "tento" or "tenhle" (with the appropriate gender/case changes), the latter being less formal.