likely to increase confusion and she may be upset for a little while but a good home will be able to manage the change with as little upset as possible. she should be allowed to keep some familiar things with her... perhaps the home that is closing would let you have pictures from her bedroom wall to go to the new place for example... maybe a familiar bedspread that sort of thing as visual clues can be useful
Times can vary... The local social services dept may be able to help you I usually takes a while as they need to give adequate time for all the clients to be relocated although the local council might find a place short term it might not be somewhere as nice as you would like. Get looking asap before others in the same boat snap up any good homes... getting on a few waiting lists etc. Best guest would be 3-6 months unless the home is in really severe financial problems
She's in good health, besides the dementia, but she's 82. She has a best friend in her home, they sit and hold hands. Splitting them up might be detrimental to her mental state.