Hi, I actually have a few questions..

First, I have asked my parents to sponsor my wife as I have been living in Thailand for the last ten years.

My father asked me if he is liable l if say my wife gets in a car accident and is at fault?

Also, although I do not currently have a job, we do own our house here, worth over $150k, and I do have a good bit of savings from an inheritance, and also have a decent potential career as a statistician. Is it possible I don't need sponsorship from my parents even though I do not have a job now?

If you have assets (savings and house) worth more than $65,000 , then you don't need a joint sponsor. As for the first question---I don't really know. The i-864 is a guarantee that the immigrant will not be a public charge. To sponsor your wife, you need either an income of just over $20,000 (125% poverty level. https://www.uscis.gov/i-864p) a year, or 3 times that amount in assets.