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?
There are multiple types of exchanges.
The biggest exchanges are simply platforms to connect users. They don't store anything. Some users will put some asking prices. If the prices are unrealistically big, they will not sell, because others will sell on smaller prices. Some other users will want to buy. If they offer too low prices, nobody will want to sell to them, since others will want to buy at higher prices. When seller and buyer prices match, the sale is done and the platform will get a small fee.
On these exchanges you can also sell/buy "instantly". In that case you'll match the highest buyer's price or the lowest seller's price plus the platform fee.
There are also exchanges where you can "trade" directly with the exchange, not other people. They have bigger fees and how they work is their business. They keep a stash, but I think that most have it small and have some money waiting on some of the biggest exchanges and when you initiate a trade, their bots will also make a similar trade on the "normal exchanges" to replenish the stash.
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?
Any trader tries to sell.buy at a price - bigger or smaller. They don't necessarily trade at the current spot price, they may wait the price rise (if they sell) or fall (if they buy). Maybe you should read about limit sell and stop loss.
I said traders. Not only miners trade.
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?[/li][/list]
The price is determined as I wrote, by the buyers and sellers expectations.
Also there are plenty of trading bots, some are arbitrage bots which will "equalize" the price between exchanges as soon as one has much different price than the others (by buying from one and selling to another).
