A roll of the dice!
Anytime you buy something from any classified source and even Ebay and such, you run the risk of seeing the things you have shown us. Porcelain is durable but can be delicate at times. The spot on the edge of the door is easily repairable and since it is where the gasket contacts the door, anything you may use will not come in contact with your dishes.
Don't start taking sensors and elements out of the sump just yet. The rust could well be just surface rust and will come off with soft scrub or Ajax or that type of non abrasive cleanser. You may want to try using ZUD as it contains oxalic acid which helps dissolve rust stains. Gently rub the area and rinse it away to see what is happening. Sometimes, chemicals in local water supplies react with the metals inside the dishwasher and there was likely some standing water in the machine for a while before it all evaporated leaving trace minerals behind.
Do pour in some water first to help "swell" the seals and gaskets, and you will also find any leaks before bringing the machine into the house.
You can do a test run of the motor by plugging it in latching the door closed and simply hitting the cancel/drain button and the timer will start the pump and run thru to the end and "drain" the machine out. That way you will hear the pump run, the drain solenoid snap open and closed and the dryer blower fan come on and know it is working.
The fuzz you have on the filter is very common and the best I have ever figured out is that it is nothing more than cellulose from paper, vegetables and meat that has been continuously washed by the detergents and has broken down as far as it can go, You will see that stuff in every dishwasher be it domestic or commercial. That is my main reason for not expecting a dishwasher to be a garbage disposer and food should be scraped off before loading. Not until Hobart put an actual disposer(though on a small scale)in their 21 and 22 series machines, did any machine have anything better than a soft food grinder. Yes, other manufacturers came up with soil separation technologies of their own but now could actually grind up hard objects.
Now that is not to say Hobart wasn't stubborn and thick headed in not having multiple rinses after their main washes on the 21 and 22's and it wasn't until Whirlpool came along and finally added a water heat delay for the wash cycles on the Hobart based dishwashers that you really had some stellar results. For the life of me, I will never figure out why Hobart resisted the market trend like that. I guess, if I ever started accumulating machines again, I would go for a KDS23 and install the electrical workings in a 21 or 22 tank and keep the Hobart pump but gain the heat delay features of the 23's that WP so wisely changed.
As far as the rust under the detergent cup goes. I will bet it is from the bottom of the dishrack. Pick up the front of the rack and look for rust and wear under the rack, in the middle and even the left and right sides in the front area. If you close the door with the rack still outside the tub, it will rub on the door and eventually wear away the coating on the rack and cause rust stains. You can see if the dispenser is leaking by removing the door panel and it will reveal all. As John L always says, take the dispenser out and turn it 180 degrees so the water if it gets by the small o-rings on the door shafts, should leak, it will fall harmlessly into the door cavity and not on to the wires for the bi-metal heaters that release the doors when the timer calls for detergent.
The water delivery tube under the top rack to the washarm will get a little softer with use. So don't worry about it now. Most of the time, they got squishy and deteriorated as the machines aged and was a common part that needed to be replaced. Look on the underside of it. There is a small hole in it to drain any residual water left in the tube. If it is looking like it is starting to crumble, then look for a replacement tube. Many of us still have some around with some life left in them. I have even seen people use the clear vinyl reinforced tubing you can get at Lowes or HD for a replacement. I don't know how long they may last but hey, it can work.
Not much you can do about the rust on the bottom rack where the hardware goes. Another fail spot after many years of wear. The previous owners may have loaded the rack with really heavy dishware and the metal is going to flex and the coating is going to give up sooner or later. Again. it's your choice to find something to use on it.
It would do you well, to try to find a donor machine to have a stock of spare parts for your machine. Racks are nearly impossible to find. But they are out there. A newer top rack will give you a wider washarm that gets the corners of the rack much better than the one you currently have. You will need to change the whit manifold in the back but it is an easy change to do. Does that cover it all? If not, we are all following this thread and will likely chime in for you if we need to.
