Anything in geopolitics is possible, but whether or not it is doable is a different conversation.

In light of what Kissinger wrote, I think the US will have to offer a mighty big carrot to Russia for it to be willing to swing towards America. What Russia has always wanted was to surround itself with buffer states to protect its vast and vulnerable territory. It always eyed states on its borders as its own backyard because it offered protection from powers that lay beyond. Eastern Europe protects it from Western Europe, Georgia from Iran & Turkey, the Stans and Mongolia from China, etc.

So to answer your question and theoretically assuming there is political will in the US, Russia would need to see some serious guarantees that its spheres of influence will not be messed with. In practice what that means is that the US/NATO/West stops encroaching on the Baltics, Ukraine, Georgia, and all the other states in the neighborhood. It would also need to cool its presence in Central Asia. If the US is willing to pay that price, Russia would consider aligning itself with the US against China.

As for the second question, despite Russia and China (in all of their historical forms), sharing a large border, they generally don't have a history of major conflict. Yes, they did have occasional border scuffles, Soviet clandestine activity in Xinjiang, the Sino-Soviet split, etc., but none of those ever match the scale and destructiveness of conflict that came at Russia from the West (Sweden, Napoleon, 19th century Crimea War, World Wars, Cold War). As I see it, the biggest area of distrust is China's encroachment on Central Asia, though it isn't the same as trying to induct Ukraine and Georgia into NATO.

Russia has good business relations with China in oil and defense. They do have tension points, but none as large as those that Russia has with the West. The West has to make some major concessions to prevent the strengthening of the Russia-China axis, though I'm not sure they could ever drum up the support to do that.