Hi,
1.If someone says 'No' politely, could we use all these terms like 'refuse' 'decline' 'turn down' and 'reject'?
Of these choices, only 'decline' sounds polite. It's fairly forma,l more for wroiting than speaking.
2.If someone says 'NO' impolitely, which would be better to use?
Of these choices, 'refuse' and reject' are quite strong, quite emphatic. 'Turn down' is slightly less strong, in my opinion, but still carries force.
I don't think people would always say "no" in polite way. That's true.
3. Is 'turn down' formal or informal? It's more informal than formal.
4.Gail invited me to go to the movie with her, but I turned it down.
Is 'turned it down' ok here? Say 'I turned her down' or I turned her invitation/the idea down'. It's OK as a way to tell me about your conversation, but it doesn't really tell me much about what you said to Gail or what your level of politeness was.
Best wishes, Clive