If it were me, I would insist that the dealer itemize and explain every fee on the lease form. Those forms are intentionally designed to be confusing and to hide extra fees from you.
The only things that are non-negotiable are the tax rate and the license fees, because those are set by the State.
Dealers don't like to negotiate the Destination Fee (shipment from the factory to them) or the Documentation Fee (to cover their paperwork costs for handling the car) or the Acquisition Fee (to cover the paperwork costs for financing). That doesn't mean they are non-negotiable, just that they are harder to negotiate.
Two things stick out as being worrisome in your description.
1. "The mileage only matters if you don't buy it or trade it in" is a very suspicious statement.
I'm not sure I even believe the first part, though it makes a little more sense. Since you have already agreed on the residual value you're willing to pay, you can pay that price for the car at the end of the lease and it's no loss to the dealership. The fact that there is more wear on the car than you agreed to is your problem, because they are getting the money value of a car with X miles, and you're gettying a car with X+Y miles on it.
But if you trade it in, they need to sell it. And it's worth measurably less the more miles are on it. So I find this statement overall to be 51% ********, and 100% ******** if they won't put it in writing.
2. "We won't negotiate on the MSRP because we can sell it above sticker to another dealership".
That's an ordinary negotiation tactic, just like "these cars are in high demand and I can sell it tomorrow at full price to the next customer". It's just not true. It's a bluff, and is an ordinary part of the negotiation game.