I recommend electrum or armory on an offline PC over using bitaddress. But since you've asked:
1. It is just an option
2. Transaction data is stored in the blockchain which is a public transaction ledger. When you send coins you are simply signing off ownership to whoever might possess the private keys behind a particular address. Meaning the address does not have to be online or even exist.
When the person who does have the private key wants to spend the coins he simply signs off ownership to another person and sends that transaction to other bitcoin nodes. Miners add that transaction to the blockchain and it is done.
3. What tutorial?? Link please.
4. Transaction data is public information as I mentioned above.
5. Never heard of anything like this. Bitaddress runs in a web browser so having an up to date web browser is more important.
It might help if you learned a bit about the underlying technology behind bitcoin. Could save you from losses in the future:
https://bitcoinspakistan.com/blog/private-key-public-key-bitcoin-address-and-the-blockchain/