To your above post - my observations are specific to the article I originally linked and the communication therein. Big picture is important but sometimes we need to look at the immediate circumstance and intent. A message can be as simple as what is written.
So to this post and the good questions you have posed, I would start by saying there is no easy yes or no. It's much more complicated than a one word answer. But I'll make an attempt to share my view as simply as I can based on where I currently see US/China Relations (China Geopolitics Thread is probably where this should be continued):
1) Yes, the US can maintain supremacy in Asia, with China actively resisting, for a time
2) Yes, China can achieve supremacy in Asia, with the US actively resisting ('impose' implies through forcible means, which is not a prerequisite for China to reach this status), in time
3) Most individual nations in Asia currently want US Security Guarantees & Access to US Markets. Most individual nations having security assurance from China & North Korea would prefer US Forces not be in Asia. Population wise (ex. if it were a vote) most Asians do not currently want US Forces in Asia.
As I noted before, China is geographically at home in the region, with it's efforts centred in Asia. It shares a common culture to it's neighbours. It has a large, motivated population and it has a growing economy and R&D base. All of this predisposes it to naturally become the leading power in Asia as time goes on. Militarily it is focused in the one region with it's local support base; not spread across the globe countering adversaries in Europe, The Middle East, South America etc. Events and how they are responded to by China & the US will dictate the timetable.