Why does bitcoin exchanges have different buy and sell price even before they add fees on top of it?

Bitcoin exchanges operate as continuous double auctions, filling an order book with sellers providing ask prices and buyers submitting bid prices. When a bid and an ask meet, the orders are filled. So you'll see the order book as a series of asks from the last trade price on up, and bids from the last trade price on down. Based on the order book of the moment, for a given quantity of bitcoin, you will always see a gap between the buy price (how much it would cost you per bitcoin to buy that quantity) and the sell price (how much you would receive per bitcoin if you sold that quantity). This is because as you buy more bitcoins, you move up the ask orders and the price being paid rises. The same thing happens as you sell more bitcoins, you move down the bid orders and the price being paid goes down. See Bitfinex BTC/USD Charts - BitcoinWisdom for an example, move your cursor over the order book lines and look in the top left for the effect on prices. When an order is filled, the exchange also charges fees to the buyer and/or seller based on the policies of the given exchange.

Bitcoin brokers are selling you bitcoins from their reserves, and they need to buy and sell bitcoins to maintain their reserve. So based on the behavior of the exchanges they use, bitcoin brokers will set a buy price that lets them replace their reserve bitcoins for the same or less than what you paid to buy them. Similarly, they will set a sell price that lets them sell reserve bitcoins for the same or more than what they paid you for them. See Coinbase BTC/USD Charts - BitcoinWisdom for a broker example, their current buy and sell prices show as fixed "order book" lines. Commissions charged by a broker are then added separately, though they can also be effectively hidden in the prices they are quoting.