1) When first generated and printed, the wallet is just a piece of paper? No connection to the blockchain, yes?
Yes.
2) When a transaction is generated and Bitcoin is sent to the wallet address, it then is recorded on the blockchain?
Yes, that is the first that the Bitcoin network knows of that address.
3) When you merge a paper wallet with an online wallet like at Blockchain.info, how does the receiving address confirm the private key printed on the paper wallet?
You "import" the private key into the Blockchain.info/wallet. That private key is then no different from any other private key in that wallet. The Bitcoin address is a derivative of the private key. So it doesn't need to know the Bitcoin address, just the private key.
4) How do you merge a paper wallet directly into a QT client?
importprivkey yourPrivateKeyInWalletImportFormat
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http://en.bitcoin.it/wiki/How_to_import_private_keys_v7%2B#Run_Import_Command_in_Debug_Window