I can add a few important things to your list. Ha ha.
1. NEVER give a salesman a monthly payment, even if you're going to finance. In fact, NEVER ever discuss monthly payments with them; just vehicle price. And only after a price is agreed upon, then you should discuss payment terms (interest, length, down payment, etc). However, it's better to already have terms from your bank (or other lending business), and only discuss terms if they can beat the interest and down payment you already have. If you tell a salesman a monthly payment figure, you'd be doomed, as they'd just get you the longest loan possible, and even tack on a kickback over the interest, until they match your figure, and make a killing.
2. NEVER tell a salesman you have a trade, until you have a firm price on the new car. Then throw the trade, to know exactly how much you'd get for it. They never like that, but that's the way to do it, to keep control of the transaction (rather than them). Otherwise, you'd never know how much you're paying for the new vehicle, and how much you're getting for your trade. And have a figure for your trade already from Carvana, Vroom, etc, to have an idea the market value of your car. You could get the tax differential less at the dealer, and the deal would be the same. But if less than that, you should just sell your trade directly to any such dealer, and buy the new car outright. Many pay you on the spot, or a few days later.
3. Never sign anything agreeing to purchase a vehicle, until you see ALL THE CHARGES first, including the infamous 'doc fee', and every other charge. As mentioned above, you could walk at that point, if needed. And never buy anything the creepy 'finance managers' want you to buy. You could buy any of those things later on if you want, and much cheaper. They push them like crazy, because they're like 90% profit for them, so be firm.
4. Finally, never fall for traps like the car is on sale just today, or there's a special just today, etc. DO NOT rush a vehicle purchase. Take your time, and do things right.