Why does the price change depending on whether I am logged in or not?
Bittylicious has multiple sellers behind the scenes, each offering coins at their own price, and with their own minimum and maximum amounts of coins they are willing to trade.
If you, for example, attempted to buy 2 Bitcoins, the price is exactly the same whether you are logged in or logged out. To prove this, type in a figure of 2 in the Number of Bitcoins field and click the green refresh button right next to Get some coins. You will see the price is the same in both situations.
The reason it might have looked different to begin with is because you are allowed to buy more coins when you are logged in. Bittylicious, by default, works out the price for you based on the maximum number of coins you are permitted to buy. For example, if you were allowed to buy 5 Bitcoins when logged in and only 1 Bitcoin when logged out, there could be a seller offering a minimum of 2 Bitcoins for a cheaper price than a seller offering any amount of Bitcoins. This would mean that the price is cheaper when you are logged in. The converse would be true of the seller offered a cheap price for a maximum of 2 Bitcoins.