If the banking system collapses, then btc price will collapse too. Btc demand is fueled mostly by wires of fiat from bank accounts from speculators.
Doubt it. If fiat currency collapses or hyperinflates, people may start wanting to use BTC to actually buy things, that is start using it as a currency. BTC price in USD will not collapse, it will just become irrelevant as hyperinflation makes it a stupidly high number and people don't bother trading in their $100,000 for .001BTC

BTC will become "priced" more in food, commodities
If the dollar becomes worth a hundreth of what it is now the price of bitcoin in dollar will increase a hundred times. The value of bitcoin is in purchasing power, the dollar price is just a middleman to make your simple monkey brain able to comprehend it.