Answer
(Fatwa: 1103/1103=M/1430)
Muslim children should not be given education in schools where the education of other religions is compulsory for students. The scholars of Fiqh have regarded it makrooh (undesirable) to visit the church, mandir (temple) and worship-place of other religions, it is explicitly mentioned in Shami and other books. Muslim children also should not be taken to temples.
(2) I do not remember any Hadith regarding the same.
(3) It is makrooh tahreemi.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband