a) Explain why the US hasn’t gone back in so long,

Why would they? Nothing of value came from any of those missions and the risk is enormous.

and why with modern technology it seems so difficult? (especially given that NASA has been experiencing numerous delays in the Artemis missions, that certainly hasn’t given them a good impression…)

Because transistors are a lot more sensitive to EM than valves. Our current technology miniaturized lots of things, but that also means that a single piece of conductive material (like moon dust) or a single electron (from an em pulse) in the wrong place can wreak havok to it. Old computers required lots more electrons and space for their actual function so they were a lot more resistent to random variations. And we can’t make old computers anymore because we don’t have the factories for them, and you’re not going to create an entire factory just to produce a couple pieces for one mission, so they have to focus on isolating and making things more resistent.

b) How do you verify moon rocks without having actually been on the moon? How did scientists figure out what a moon rock looks like?

The moon is constantly being bombarded by unfiltered radiation because of its lack of atmosphere. This makes it so they’re composed of minerals that rarely occur on earth (they usually bind with oxygen or nitrogen in the atmosphere), have different isotopes (because of the radiation) and are much older (because no interference from tectonic movement/rain/wind/etc)

c) Why aren’t the old Apollo designs being reused for a moon landing? (by either the Americans or the Chinese)

Because they can’t for the same reason the US can’t, they don’t work with modern electronics, and no one can produce old electronics.

They say that there isn’t strong evidence either side (but believes that it is false, saying that “we will see” once someone else lands on the moon)

There is very strong evidence, your friend can corroborate for himself by spending a few thousand dollars (or he can understand that if anyone wanted to they could). First you need to buy a very powerful laser, then a very sensitive sensor, you hook them so they very close together and fire at the moon, you will never get a reading back, because the moon surface is a difuse reflector with a rough surface the light will scatter and go everywhere. However, when the astronauts went to the moon they left retroreflectors in specific locations, so if you pointed at one of those you would get the signal back approximately 2.5 second later.

And what other points can I bring up to definitively say, yes, the moon landing wasn’t faked?

I guess it’s easier to ask them “what evidence would convince you” because the answer will be none, of there was any evidence that would convince them they would have been convinced already.

Another thing, they also can’t believe that astronauts could bring and ride the little moon buggies. I am also partially interested in how that was achieved to be honest!

Not sure what’s there to not understand about this, so I’ll just say same way cars get to a dealership and you ride them afterwards.