Which part of the iPhone 8 Plus is this?

Solution 1:

That looks like the gasket holding the touch chip in place on the original screen assembly, fastened on the metal shield that you transfer from the original assembly to the new one. It is there because the touch chip needs to be in a very specific position to fit down in the phone when closing it. It is however not necessary for operation.

As for the ear speaker and light sensor not working, those are either the result of incorrect placement of the sensor and speaker contact as part of that assembly, when you transfer it from the old to the new screen assembly, or you have damaged the assembly itself, which is very easy to do when you are inexperienced, as it is a delicate part.

The home button part is also delicate and it is somewhat easy to rip its flex cable close to the contact when lifting it off the old screen assembly, which could give the symptoms you describe. Otherwise, try to reseat the contact.