If I may, I will try to answer your first question as simply and clearly as possible. It is clear that the term "allophone"—which originated in Quebec, by the way—has Greek roots. "Allos" means "other," and "phone" means "language." Moreover, sometimes people use "other mother tongue," that is, neither English nor French, but a mother tongue other than English or French. So it can be very technical.
The second part of the question is that, in principle, if both English and French are used equally in the home, people will indicate "French and English" on the census form. If French is used more but English is also used regularly in the home, respondents will indicate "French or English" in response to the second part of the question, which asks whether other languages are spoken regularly in the home.
Although it can be confusing, Statistics Canada collects this information, and people can decide whether someone who uses both languages regularly at home should be defined as bilingual or as someone who is francophone or anglophone. It is quite involved, and people choose option A versus option B. People interested in the situation of francophones outside Quebec will classify those who speak a language other than French in the home as being francophone. If I am interested in the situation of anglophones, I will put them with the anglophones.
So people choose how to use this information, but when you fill out your questionnaire, the question should be clear, in principle. If you indicate both languages, it means that you use them equally. Other people do not decide for you whether you are an anglophone or a francophone.