Brass colored piece is a bracket / clamp / mount to hold a water inlet valve in place.

It was probably dropped there during replacement of a water valve, if it has never had a valve replaced then it was dropped there at the factory.

That smashed connector on the pump connection - that looks like damage from failed or weak shockers. When the shocks get tired, the drum jumps around more and bangs into other components and breaks them.

Is your pump 120 Volts or 240 Volts? If 240, I can measure something similar and let you know how many ohms it is. If 120, an American person could do the same for you?

Can you post a clear picture of the whole pump? I think Miele pumps are fairly generic - the front housing with the coin catcher inside will be unique to Miele, but the back half, the motor and impeller, is often a generic European pump. You might be able to swap in a replacement back half?? (much cheaper than genuine, quality will be the same.)

Your photo is hard to make sense of, it is so zoomed in on the connector, but it looks like the white cover has broken off the pump?? To be worth testing, that would have to be undamaged. You can test the pump simply by applying the required voltage (AC 240V or AC 120V) to the pump terminals, with the pump removed from the machine. I'm not going to tell you how to do this, if you don't know already then it really isn't safe for you to proceed. This is lethal voltage you are dealing with. Please take great care.

I don't know the W1918 but older Mieles used to open at the front for servicing - amazingly easy to do, after removing some bolts the whole front panel hinges open like a door. If the w1918 is the same it should be easy.