Tesla PowerWall best use in Louisiana: EV charging? Emergency generator?

1) Correct, linking them together increases ability to handle surge and steady loads. Once you get to two you can handle things like dead loads better. Over two your just adding power to use more power. I’ve always seen two as ideal so you don’t have problems with multiple appliances surging together.
2). I only know a little about this but assuming you wanted A/C along with critical appliances, I’d say two depending on how hard you ran is (summer or winter in La?). Could maybe get away with 1 if you only ran the a/c and very little at that.
3) yes if you can get a big enough array. And I don’t mean you need something massive. The house just needs to be oriented decently, have enough roof space or have enough space for a ground mount. 120% offsets are not uncommon.

What’s the end goal here? Isn’t two units like $15k installed? Then you need a shitload of solar panels, so add another $30k. Even with a $200 electricity bill the payoff would take 19 years. I’m sure everything would have fallen apart or failed by then.

Well they market the Powerwall for this exact purpose.

Apparently it would take 3 to provide backup power for my entire house for 1 day.

I think if you go to the website there is a calculator. I got something like 60k for cost with a savings of 18k in 20 years