- The exchanges purchase a bulk lots of Bitcoin that they can sell on there exchange, or do they have a list of traders/wallets willing to sell that they transact with when I click the buy button?
Exchanges don't purchase any Bitcoin, they manage it as the middleman for the transactions. Imagine a convenience store, you buy something, the cashier is the middleman, and the product is given to you through the purchase you made to the middle man by paying it. Literally anyone who has any amount of crypto could be the person whom provides the exchange with the volume of coins they show to their users.
- Do the miners somehow set a 'reserve' price at which they are willing to sell, or is the price of one BitCoin defined somewhere else by someone else?
No they don't. Their just like any other trader here, where they sell their BTC close to the set price of the market, or larger if they are willing to wait anyway. They can be called the source of BTC, but they don't set the price. In the first release of BTC, sure it could be said so, but it's been 10 years, BTC market has a lot of it flowing through the exchanges already.
- How do the various exchanges determine the price? Whats to stop one exchange selling at $5000 and another for $3000? How do they synchronise their pricing and why do they differ slightly?
They don't synch it. If someone lowers their selling price, the overall average of the price of the coin lowers, but that only stays for a moment since I mean, who would do that right? Exchanges right now don't differ much in terms of price and even if they do, it's because of the amount of volume of coins that are being traded in their respective exchanges.