Modern cars have a cabin air outlet. It's usually hidden in the trunk or the back of the cab (on trucks), and vents somewhere like behind the plastic bumper. There are rubber flaps on them to ensure one-way air travel and keep water out. Perhaps Tesla's has a motor on theirs to keep it closed against the increased cabin pressure.
Just by pumping air inside through filters a positive internal pressure is automatically created. How much pressure will be created is proportional to the pump's flow rate and inversely proportional to the car leakage constant ( I think it's something like leakage ~ k * P.I.P., which would make P.I.P. ~ pump flow/k ), but some positive internal pressure is a given even with those outlets.
Probably depends on the bioweapon. For instance, I'd expect it to be effective against anthrax spores, which was the most recent bioweapons scare we had.
You're still using outside air, but by maintaining positive pressure you ensure that it's only coming in through the filter, rather than a mix of air intake and leaky joints.
Not sure about particular type of filter, but CBRN countermeasures found on tanks, APCs and such are also basically air filtration with positive internal pressure.
It absolutely is, but that doesn't mean it wouldn't work in principle.
A HEPA filter is used in a lot of labs where biological substances are handled, even potentially hazardous ones. It should filter many types of biological agent out of the incoming air, and the positive pressure will keep such things entering other ways.
I think the reason they put it in is so people would talk about it and, look, we are. It is a marketing gimmick that likely doesn't require any additional hardware in the car (the air pump and HEPA filter are already in it, this just turns the pump up and adds a new dash button).
I'll give Tesla the nod for one thing: They sure know how to market. Between the wing doors, the bio-protection mode (which will be on the nightly news), and insane mode they're very savvy.
They are probably storing compressed air in the cabin. You start the bioweapon-defense-mode, the fan raises the pressure in the cabin ( that uses outside air) and then shuts off. (Or they store a little bit of air somewhere, perhaps for the breaks, and use that.)
