it will generate those paper wallet without asking how much I want to put on it? So what amount is associated with those addresses? Clearly I didn't put anything on them. Try it.
I don't need to try it.
your wallet is the privatekey.
..
The balance then is simply the sum of all transactions.
The blockchain that the clients download, is a history of all transactions.. that's why there's a worry about the size of that. The paper wallet doesn't hold an amount, it allows you access to the account - that is, it allows you to action change in that account, which is the same. You then think that you own something called a Bitcoin.. but your don't own some-thing, you own an idea - that idea has value and that idea is money in your account. Money is an idea, a confidence that tomorrow you can spend what you have today... it's simply a medium that people agree on exchanging.. and that then communicate wealth. Wealth matters; money does not.
To check your account you can put the public address into
https://blockchain.info/ Do not ever post your private key to an online website!
Some third party sites will store the private key for you; you will have a public address and a more traditional password - Andriod blockchain.info app does that - but that's not as secure because you are trusting that 3rd party.. blockchain.info is probably ok but still not as secure as d.i.y.