Russia and China are natural rivals and a scenario in which Trump-led American FP aligns closer with the former against the latter is not unthinkable.
Not happening.
Since 1991, Russia and China have slowly strengthened their strategic relationship. China aims to get everything it needs from Russia through trade. Everything Russia needs such as the gaps in its technology and investment requirements can be met by China. China depends on critical Russian technology for its military.
Its a marriage made in heaven and it accelerated because the West acted provocatively and threatened both Russia and China. NATO expansion and the Pivot to Asia are just two examples.
This alliance checkmates all the attempts at encircling both China and Russia and the nightmare of Sir Halford Makinder who clearly represented the British empires strategy of preventing such a union in Eurasia.
The US inherited Britain's role as a maritime power and they dropped the ball when they created conditions that allowed this alliance to happen.
Trump has nothing to give Russia. The sanctions might have been one of the best things to happen to Russia in terms of diversifying their economy. According to estimates, the economy will be back to growth this year after the recession. Pro-western oligarchs who are allowed to own some media in Russia are hurt by sanctions and are upset. The average person on the street has faced hardship, but they have been told that its due to sanctions so they are rallying behind the flag.
The Russian government does not want sanctions lifted for another few years, and they will drag their feet on their own counter sanctions
because it keeps out price dumping of agricultural products from the EU. Russian agriculture exports have boomed during the sanctions.
The US has weak cards to play, there's a short term window of technological superiority another 10 years max. The Chinese are getting aggressive because they know they can fight right now but it will be too costly. In the early 2000's a war would have been a cakewalk at sea and air for the USA just like the 1991 Gulf War.
Today China can hurt the US bad, probably wipe out 2/3 of the pacific fleet for horrendous losses.
The Russians talk more, the Chinese barely talk much. Putin remarked a month ago of the relationship between the two countries being much more than strategic.
No matter what Trump or Bannon think, they aren't breaking up the marriage of Moscow and Beijing. And the US isn't going to war with Iran without those two along with other countries such as India, Turkey, and South Korea throwing a fit due to trade relations.