Yes, The official documentation is quite outdated, even the images are from versions before Electrum transition to PSBT workflow.

Unfortunately, there's no Electrum feature like that.
You can create multiple wallets in Electrum and it loads the last wallet that you've opened you can utilize that to show that you only own that amount.
But attackers may know it that they might just force you to show your recently loaded wallet list.

No fees only if the recipient is the owner of the other end of the payment channel you've used.
If the payment requires routing through other channels to get to the recipient, there's be minimal fee based from the routing channel owners' rates.

As for Electrum's lightning implementation, it's self-custodial so you'll be the one who's in charge of managing your channels and liquidity.
In other words, you wont be able to use lightning right off the bat.
You'll need to create a channel by spending some of your on-chain funds, then manage your channel(s)' liquidity since you'll only get outbound capacity upon establishing a channel.
More info in this thread: Electrum Lightning Network walkthrough

And this topic may need its own thread.