Hi. Electrician here. The dryer outlet without a ground is perfectly fine to use to charge the tesla. Old dryer outlets had the case of the dryer bonded to the neutral of dryer, as the dryer required 110v for its lightsgue and timer circuits. However, the neutral wire of the circuit is bonded to the ground at your panel. Because the tesla charger does not require a neutral, you can essential treat the neutral eire as a ground wire in this case.
The goo is definitely anti oxidation compound, which is perfectly fine. My only concern is now that you took the outlet out, making sure you have the correct torque on the screws is important, most homeowners do not tighten them enough, and that will result in a fire.
Choice 2 is the better choice because it will ground the tesla charger, despite the fact it is using the “neutral” conductor.
You definitely do not need to run a new wire, but the extension cords will really need to be monitored and replaced at the first sigh of corrosion/damage