Q: Do purchases show in my purchase history if there was a store credit balance from a gift card?

All items that are bought on your account should show on your purchase history, whether they were bought via a credit card, your account's balance, both (e.g. if a balance doesn't cover the item's price) or if they were free. You can't see a list of when gift cards were redeemed, nor how purchases were paid for, you can only see the purchase history.

Purchase history : log into your account on your computer's iTunes via the Store > View Account menu option, you should then see a Purchase History section with a 'see all' link to the right of it. Click on that and you should then see a list of your purchases

My account's balance shows at the top left of the store's page on my computer's iTunes, and by logging in to view my account via the Store > View Account menu option. On my devices it shows at the bottom of, for example, the Featured tab in the App Store app under my account id (or you can view your account via Settings > iTunes & App Stores and it should show on the screen that you are taken to)