How can I see the history of my gift card redemptions?

True, they don't show redemption history directly.

But, if you're looking at your list of purchases, when you look at the detail screen for each one (whether in iTunes or in email), the payment method will be shown. It will either be a payment card in your account, or the words "Store Credit". It's cumbersome, but if you go through them one by one, you could identify all purchases that were billed to "Store Credit", i.e. the ones that consumed the balance from your gift card.

It's not currently possible to see a list/history of cards that you've redeemed. If you think that your balance is lower than it should be then you could try contacting iTunes Support and see if they can help : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then Purchases, Billing & Redemption

Same problem here. I reset my password and they reduced my balance by a dollar. I've been in contact with support and they just keep telling me to review my purchase history. After 3 rounds of email, they told me my recent gift card (unspecified amount) went on a balance of $0.00. Which means that their numbers don't add up.

it seems that whenever i purchase an app, it takes of more money extra. sometimes its 2 dollars extra, sometimes its $5!

Depending upon what country that you are in you may also have sales tax added to the item's listed price.

If using a credit card and you change or add card details when doing the purchase you may also receive temporary store holding charge(s) :iTunes Store & Mac App Store: About payment card authorization holds - Apple Support