If everyone decided to switch to Bitcoin tomorrow, how much would a Bitcoin be worth? Hypothetically, if everyone decided to trade in all their money and get Bitcoins for them tomorrow then how much would a single Bitcoin be worth?

My dodgy calculation makes it out to be $3,750,000 per BTC since there is apparently $60 trillion worth of fiat money and there are almost 16 million Bitcoins in circulation however I'm sure the calculation isn't that easy :p
What complicates your calculation is the liquidity aspect.
Although there is about 16 million mined bitcoins, the number of bitcoins available for trade is far less than that.

What is interesting to observe is that the fact there is a ~7bn market on bitcoin right now doesn't necessarily mean the sum of the money spent by the bitcoin holders is even near 7bn. Some people bought if for pennies, some for a couple dollars, some mined it. It just means that the holders of bitcoins are not willing to give them away for the price being offered by buyers right now.

The price is determined by supply and demand market forces, and the supply would respond to the increase in price. I maybe would sell one of mine if the price reached $100k per unit.

Other factor is that fiat money may be created out of thin air, so it has sort of an infinite supply. If an unrestricted government decides to purchase bitcoin, this would strongly push the price up.

In the end of the day, what you can try to grasp is what would be the minimum price it would reach, but estimating the actual price would depend on far too many variables.

Note that non-Bitcoin currencies have the same or extremely similar price mechanism. Dollars, specifically, can lose all their value if people stopped liking them. In a way, cryptocurrency is a huge threat to "free floating" currencies like the US Dollar.