Whats the inflation rate on fiat currencies 
I think it depends on the currency. Try googling it, there should be a lot of results.Meant in the case of a currency collapse or high inflation bitcoins will hit 1K pretty dang fast relative to any one currency
I would still be difficult for all currency pairs to collapse in unison. Governments own a lot of fiat currency (not just their own) and will always need to exchange this currency reserve for there own currency. In this way a lot of value can move between fiat currency pairs. So it is relative and not all pairs can devalue unless Governments decided to hold Bitcoin as a reserve currency (not impossible buy unlikely).
Well the topic said will bitcoin reach 1000 one day so yes it can if any one currency collapses vs a full basket of different currencies is a different scenario
If inflation is at 10% a year it would reach 1000 faster than at 2% a year assuming bitcoin keeps growing against any one fiat currency
With less units being created in bitcoin causing appreciation of each unit of bitcoin if the value of bit keeps growing in total value over time