hello rocky2012 - you need to look in the "build" menu: the last tab (with the little grid on it) is where you'll find expansions. fulfilling the quest makes it available, but (if memory serves) you still have to pay for it. you can choose to pay either in coins or in diamonds (the price buttons make it look like you need to pay both, but it's either/or).
the inventory button isn't used for anything yet. we'll see what it's for when the developers finally implement it.
and while you're in the forums, i recommend a good browse through the "guides" section - it's full of really helpful information.
enjoy the game!