bitaddress.org already provides your private key in Wallet Import Format, which is encoded in base58check format.
In the example screenshot below, the base58check-encoded WIF private key is KzNKqwBPaVehsA2F94n9UJ5mrkM9NazBjqBBwsb2U9pAGLdc4md3
To address your "rule 1", the most secure way to handle this data is load Electrum onto an airgapped ...
Later I read that it's impossible to transfer bitcoin between those two kinds of wallets. Is it true?
This is not true.
However a wallet needs to know about Segwit addresses in order to be able to send to them. Since it is a new address type (well new when it was introduced 3 years ago), software that hasn't implemented it yet won't know what to do with it.
The design/structure of a paper wallet is not something is set in stone, but the main idea is writing public and private key pairs on a piece of paper.
The universal flow for generating an address is:
A public key is derived from private key
A bitcoin address is derived from public key
The common flow (Mnemonic) for generating an address is:
Just to be clear/nitpick, the products you've linked to are designed to act as highly resilient physical backups for a bitcoin wallet. It doesn't really make much sense to refer to these metal plates/etc as 'metal wallets', as they cannot perform any normal wallet functions (send, receive, etc). Rather, they are just a way to store a backup for the seed that ...