I'll address your points, in order.
1) You should have an L shaped bracket with a short piece of rubber that slips over the smaller diameter protrusion, at a right angle to where the hoses attach. That keeps the pump stationary when the crank is turning. It's a factory installed item and if it's missing, contact the dealer and precious customer to find out why it's missing, who removed it and why they left it out. If you don't get one from them, buy a new one- it's needed.
2) That impeller actually doesn't look very good. The fact that all of the vanes are there doesn't really mean that much. If you look at them from the edge, you'll see that there's a kind of bulge where they pass over the slots in the pump body and a fresh impeller will never have them. Also, if you look at all of the vanes, they're angled and that means it has been there for quite a while. If you have a new impeller, or have handled one, you'll see and feel a big difference. If you press on the vanes to lay them flat, it will take very little effort and it takes quite a bit more to do that with a new impeller, as it should. Since the water will be pressurized when the pump is turning, weak vanes will allow water to bypass the vanes and you'll never have good pressure and flow rate.
3) The inside of the pump cover looks odd and the ones I have seen were clean brass with rotary marks from the impeller, not black and funky. When you removed the cover, did it have a white, thin gasket? That should never be omitted. If/when you get a new impeller, get the kit that comes with the gasket and buy a spare gasket. For that matter, I recommend having a new impeller in the pump and a spare in the boat. For the low cost, it can save your vacations and potentially, the motor.
4) Pretty self-explanatory- it failed and if the raw water pump bracket was missing, it contributed to the failure.
5) If the stuff in the bins wasn't moved, he couldn't have inspected the raw water pump. The only way he could have gotten in there is by either removing the side panels and crawling back there or by pulling the pin that attaches the sun deck to the ram and laying it back, preferably using a rope to keep it from flopping back all the way. Ask him specifically if he opened the sun deck more than it does by using the ram. If he says he didn't and is a big guy, there's no way he would fit without removing the stuff and the side panels. Look at the pivots for the sun deck, to see if it has stress cracks in the gelcoat.
If they admit that they didn't actually remove the cover, they didn't earn that $350. The worst part is that overheating that motor is really bad for the heads and you may need new exhaust hoses. Squeeze them along their length to see if they're soft and kind of mushy. If they're soft, they have been damaged by the heat from the exhaut that blew through there with no cooling water.
Curiouser and curiouser, eh?