3. I don't think there's a way to do that.
2. Wallet > Private keys > Export.
1. You can't export all public keys but there's a way to get all of them, and that is by opening the wallet file in a notepad (you'll have to remove the password). The public keys are listed inside. If you don't know where the wallet files are just press CTRL+O and copy the directory.
Ya what you told is correct on one shot you cannot copy all wallet private keys and public keys. and even the wallet address are changing on each transaction so i dont think that you wont be needing the empty address which are left unused.