Yes, this is true. However the British remember whether our clocks go forward or backwards by one hour at the end of March and end of November by saying "Spring forward and Fall back"

Yes and no. Language is never quite that simple, and the US/GB distinction is never as straightforward as people think. American English uses both words, but most commonly 'fall'. AE speakers say 'fall' for everyday use, and 'autumn' to sound romantic or poetic. It's typical, I believe, for American English speakers to talk about the beautiful 'autumn colours' that you can see around this time of year. So, even though 'fall' is the word which AE speakers use most of the time, this does not make 'autumn' a specifically British word. For Americans, it's just a less common alternative. In British English, we always say 'autumn'. Nobody says 'fall' in Britain. The only exception is the little mnemonic which Norman mentions above, and British children who haven't picked up 'fall' from American TV might need to have 'fall backward' explained to them. That said, most people are aware that 'fall' is used in American English.

Autumn is more used by British people, and fall is more used by American people; however, you will hear both American and British people use them. Hope that helps.

You will never hear a British person say 'Fall', unless they have lived in the US for some time, have American family, have a connection to America or whatever. It is of course completely understood however. In the US 'fall' is the much more common way but I am given to understand that 'autumn' might be used if they want to sound more literary.

Personally i prefer autumn coz its unique and it cannot be confused. meanwhile Fall is a homonym(a word with same spelling but different meaning), it may not be confusing when used in context. But there is a chance that "fall" may create some confusion.