As far as I understand, helium is a non-renewable fossil resource. So a sustainable airship design should be using hydrogen instead. The challenge is to make it safe.
No it's a by-product of decay of heavier radioactive elements. It's often found dissolved into fossil gas deposits, but it's not a fossil resource.
Therefore the best solution is hot hydrogen.
On mars this could work.
The brain confusion that a room of vacuum is lighter then air and will therefore have a lift is amusing.
He's saying that a bag that contains only vacuum would be the lightest, but as it contains nothing, it would just collapse into having no volume due to the atmospheric pressure. That would obviously provide no lift. As such, you need something in the bag that will fill the space.
Helium deposits don't originate form organic matter, so they're not fossil.