Wrong. Myanmar - US reconciliation occurred in part due to Indian intervention. What you have failed so far to draw attention to the fact is that the so called 'axis of democracy' is in fact a multifaceted movement wherein India is also playing its part in promotion of democracy by diplomatic and political means. Myanmar was a case wherein an active Indian intervention has bought changes which were unthinkable a decade back. As part of the same, in tandem with US India is actively involved in promoting and strengthening democracy in countries where it is in threat. Engagement with Pakistan should also be seen in this light. By not denouncing the proclamation of assured action by PM of Pakistan, GoI is simply strengthening the standing of the GoP in international arena. The aim is to strengthen the civil establishment in Pakistan and at the same time try and reduce the power that the PA has in foreign affairs. It is a two pronged action wherein even US is involved. The same can be seen from US comments in the past few days.
Similarly, the game is not between US-China as you have been highlighting, instead it is indeed between India and China in IOR and littoral. The US had 'handed over' the Malacca's to Indian Navy when their assets were required for Op Enduring Freedom. Insofar, the US wants India to shoulder additional responsibility in Pacific too, something India has no immediate plans to do. But with India now including South China Sea in the littoral, we may see some more moves yet.
The official mandate to Indian Navy by the GoI is to ensure protection of SLOCs and freedom of navigation in IOR and littoral along with power projection and ensuring dea denial capability for hostile forces. The Indian Navy has been involved in missions conforming to these parameter for quite sometime. These parameters are in sync with US parameters. One also needs to remember that both India and US have an understanding in PSI, wherein we board suspected ships even in high seas if there is suspicion of violation of MTCR, CWC, BWC, NPT etc
There are members who are portraying their inhibitions regarding the equation of Indian and Chinese navies. As long as there is conformation in navigation to the International Maritime Laws, Indian Navy will not deny sea to any nation, even if it is North Korea. However, any non-conformation will be dealt with under mandate of International Laws, something that will have support of the International Community. China is not and will not be an immediate threat for India in the near future.