Learn English – shorter term for “divided by” in American English

1. What is this "Official" of which you speak?
2. Yes. It's a perfectly common phrase in the UK, with variants such as "Budge over" or "Shift over" having the same meaning. I can't speak for other countries, but I have no reason to suspect that it's limited to the US and the UK.
3. Not really, no.
4. As per 2, I'd expect most native English speakers to recognise it, though I could be wrong.
5. Again, what do you mean by "official"? The English language doesn't have a governing body in the way that the Académie française tries to be for French. Dictionaries follow usage rather than defining it. I understand "Move over" as meaning "Move aside," such as to make space on a sofa or give the speaker access to a computer keyboard.

"Move over" on its own doesn't imply motion towards anything, just (short) motion away. You could say "Move over to [somewhere]," but that's a different construction.

In Standard English, this usage of the word times is considered an error. It is often used by children and students when speaking of multiplication, for exactly the reason that you indicate: the formula X times Y equals Z has spawned the creation of a verb to times meaning to multiply.

However, using this in any kind of formal context is considered an error, and I have only ever encountered this usage from children. I would avoid it in writing altogether, and discourage students from using it.