Translation:The children saw the old Catholic Church.
Yes for the first one, no for the second :)
"the old Catholic church" is what I would say.
("the old catholic church" would mean "the old church which is for everyone" - with the rather rare English word "catholic" - rather than "the old church where a congregation of Roman Catholics meets").
Actually the word "ναός" is more often used to describe other religions' temples, while "εκκλησία" is mostly restricted to christian temples. An ancient greek temple would be described 99% of the times as "ναός", but never as an "εκκλησία". You may say a Buddhist "ναός" but you would never say a Buddhist "εκκλησία".
And then of course one can always opt for the specific term of each religious building: eg. Pagoda= Παγόδα, Synagogue= Συναγωγή, Mosque= Τζαμί