How are certain technical words used in British English?
Britons say refactoring code rather than refactorising code and certainly not refactorizing code, to the extent they say such a phrase at all.
Both are used.
"The entertainment programme" is slightly unusual as a phrase in this context; the issue is not with program(me). The following is certainly correct: "I have written a computer program to suggest a schedule of television programmes to record".
1, factor is a verb as a specific maths term in BE. BE tends to avoid "izing" endings - like AE burglarize.
2, Indices is correct if you are writing a textbooks, but indexes is used.
3, Program = software, Programme = TV. No good reason, it's just one of those things