Yes, the turn would go something like that. Though you would need to roll 1d6 to see if you can react. If you fail, you can't do anything. If you pass but fail on the actual reaction, that might be when you take chip damage. Or you can forego reacting entirely.
1. If a player is rolling an even number of dice and gets the same number of successes as failures, how would you handle that? Would it count as an overall success?
I made a typo and put + number of dice when I meant that it's just that number of dice. So someone with a TAL of three would roll 3d6. As for same number of success and fails on say two dice (say a 1 and a 5), take the success.
2. For damage, especially reaction damage, is the d6 rolled again or would it use the same roll as the reaction? Like in the example above, would Player 2 take 2 damage or would they roll again to see how much damage they took?
They would roll again to see how much damage they took. (ex: Player 2 succeeds on the ability to react roll, but fails on the actually reaction part and gets damaged so they roll 1d6)
3. How do malfunctions and bonuses interact with each other? Let's say if Player 1 rolled 1, 4, 4, 6. My assumption is that they would succeed, go farther than normally possible because of the 6 (like maybe move up 2-3 places instead of just 1), but their vehicle sustains some damage from being pushed too hard because of the roll of 1?
So in the example you gave, the six means they succeed and get to take a bonus action (either accelerate again, attack, or handling). But on their next turn, they'll only get to roll 2d6 for their turn (it could be flavored as the turbo overheated and doesn't work as well for a bit)