Recommendation: Do your own work on your own vehicles. Research on the net, find the problems, watch a few YouTube videos and learn. You'll have to buy your own tools and you'll always have the experience to do it again. Those tools can make you a few bucks on side jobs, like working on other's vehicles. For more complicated jobs, video yourself taking things apart, so you know how to put them back together. Treat the camera like a child and show it what you're doing as you go.

It depends.

There have been cases that have gone both ways.

Recently there was a case where a mechanic at a dealership failed to torque the lug nuts on one wheel on a vehicle and it fell off causing damage. In court the mechanic admitted that they forgot to torque the lugs. The judge ruled in favor of the dealership because the dealership attempted to make repairs. The owner of the vehicle didn't even get their money back on the tire rotation.

https://youtu.be/JgmHxSKHpgc

You can sue a ham sandwich, but what will you get?

The best possible outcome are damages, which would be paid by the mechanic's insurance company. Assuming, of course he had liability insurance. The problem with assessing damages is the insurance company will only pay to make you whole. That could be a few thousand bucks. So yea.

Upon careful review, it was caused by a mechanic

How would you know? You had to take it to the mechanic in the first place. Now you are an expert?

I can believe the brake job got screwed. But the axel? I highly doubt it was the mechanic that cracked your axel if it's cracked at all. You have no recourse. You signed on the dotted line and you didn't read the fine print. I know this because you are here asking. If you had read the contract you would already know the answer.

Take this as a lesson. Never trust large chain stores. Never trust niggers. Learn to fix it yourself. A brake job takes about an hour and requires nothing but standard sockets and or wrenches.

3rd party arbitration or small claims

Did the mechanic or the shop admit they were at fault? If not, you'll have a hard time actually proving to a court that it was their fault. If it had failed right after leaving the shop you would have a better case.

Also, if you're not going to do the work yourself, a big chain repair shop is the worst possible option. These guys are the mechanics that aren't good enough to get a job at a dealership. I used to think they would fuck up cars on purpose just to get more work, but then I realized they just rush the job and don't give a shit that they might never have done repair on your model car before.

People trash dealerships for their sky high prices for maintenance and repairs, but they're usually pretty reasonable when you're looking at something more complicated, plus they'll guarantee the work. I'd never take a car in for a simple oil change or brake job though. For their prices, I could literally buy all the tools I needed and high end oil/brake parts everytime I did the job myself.

I went to one of those big chain places

On the paperwork you signed when you paid for the work contains (((fine print))) that either indemnifies the company from suits like you want to bring or contains an arbitration clause that basically fucks your legal rights over with no lube. Their jew lawyers have made sure you have no legal recourse for their nigger-tier work that caused you damage. So goof luck with that.