At the time of Alexander, China was going through what is known as the "warring states" period. At times China reached out and asserted authority in Central Asia. But that hadn't really been done yet. It would be another couple hundred years before the Han started expanding into Central Asia and really established the Silk Road. So trade through the area was sparse and highly intermittent.

With his conquests bringing him into India, was there any interaction with the seat of power in China?

Not really. There wasn't any official contact, and at the time there wasn't even a central power in China to contact.

Were they aware?

Maybe. Herodotus talks about the Hyperboreans, which some scholars like to connect to the Chinese. The Hyperboreans are placed in roughly the right place, and it's vague enough that maybe they could be Chinese. But even if the Hyperboreans are the Chinese, they've clearly gone through a game of telephone. Herodotus didn't talk to anyone who had been to China. He clearly was getting his info from people who had talked to people, who had talked to people, who had talked to people who had been to China. The best info the Greeks/Macedonians had was that there were stories that a populated green and pleasant land existed on the far side of the steppe.

Was there trade through an ancient version of the silk road?

No, not yet.

Did Alexander ever express a wish to move his forces towards China sometime in the future?

Not really. The steppe seemed vast and uninviting. Alexander did have goals to conquer to "the Outer Ocean." But that seems to have encompassed at most the Bay of Bengal on the other side of the India. I suppose you could consider China to be covered in the goal to get to the Outer Ocean, except there's very little to support that Alexander was giving much credence to the idea of the Hyperboreans existing when making those kinds of statements. The steppes and deserts of Central Asia didn't seem to interest him any further than the Hindu Kush. He grabbed what the Achaemenid Persians had in that direction and then stopped. There isn't any evidence that he had plans to go any further in the direction north of the Himalayas.

If we pull back our focus and take a birds eye view, there's one interesting historical tidbit of how Alexander's conquest came to influence Asia: buddhist statues.

Hellenistic art often showed realistic depictions of people and gods, including realistic statues. After Alexander had conquered the Persian Empire, the regions comprising it came to be ruled by a Greek class (for a time, at least). One of those regions was Bactria, roughly modern day Afghanistan. Buddhism had a strong presence in that area, and centuries of interactions (the Greco-Bactrian kingdom would survive a surprisingly long time, even spreading into India) between the Greeks and local Buddhists would lead to them emulating Greek styles of art in their own religious practices.

From the Greco-Bactrian kingdom (and its successor the Greco-Indian kingdom) statues of Buddha would spread amongst practitioners throughout South Asia, Central Asia, and eventually, China. So every time you see a Buddhist statue in China, you can indirectly thank Alexander's conquest for that.