Gas from a top tier station such as Shell, Valero, Chevron, etc. 93 is preferable, but 91 will work. Naturally aspirated there really isn't a need for an octane booster. If you decide that you just want to run one, Boostane professional is great.
They shouldn't give you any trouble due to the suspension mods, but might not warranty it based on what they think caused it to tear. If it is due to the boot being defective, then they will warranty. If they think it got torn due to road debris or something, then they won't cover it under warranty.
Is the relay bad? Have you tried putting a new one in? I would think that this might be a possibility if as you say it is getting power to the relay, and you can bypass the relay and start the car.
Here is a picture of what happens to a sidewall of a tire that is driven on with low or no air pressure shortly before it comes apart like the ops did. When the pressure gets low enough, it has to support weight that it wasn't designed to at low or no pressure. The line that you see worn into...
I'm not sure you'll get far with a claim against General. What happened to your tire is not a defect. It was caused by driving on it for an extended period with low, or no air pressure in it, which caused the rim to cut through all of the cords in the sidewall, and when it had cut through all of...