I think you are interpreting China's unwillingness to get dug into a stalemate (or escalated war) over the Doklam issue as a sign of weakness or incapability. Perhaps it is simply because resolving the issue by force isn't worth it. At the moment, the area is still disputed and China has got other ways to do Belt and Road. It isn't worth going to war, even one that can be easily won (let's assume) just to build some roads that will not survive anyway. I don't think you should read too much into that. You have concluded that China can't fight simply because they don't want to fight over Doklam. Doklam isn't Indian or Bhutanese so there is no "kicking us out" because you are not there. No one is and the issue has de-escalated and back to usual status quo. China wished to build roads through that area as part of OBOR but instead of fighting a potentially hazardous war, it has elected to pursue OBOR without involving that area, to the satisfaction of Bhutan and India as well. If one wishes to consider China avoiding war by diverting road building as some sort of victory, that would indeed be quite pathetic. No country on earth wishes to go to war over a road that is the tiniest fraction of an economic objective. If any of them wishes to use military force and take it, China will almost definitely fight. I think that would be the real test. Alas neither India or Bhutan have taken sovereignty so that issue remains in the air and certainly no conclusions about anyone can really be drawn.
As for Pakistani and Indian skirmishes in recent months, nothing has escalated either. Few tit for tats now and again but the real test would be to see if any side escalates. Neither has so again no conclusions can be drawn about the overall ability of their militaries. Inflicting serious casualties on Pakistan is hearsay and there is no evidence apart from some word of mouth from very biased sources. Even if they are indeed true, it doesn't speak much about IA being able to use soldiers to gun down some untrained and unorganised fighters. The only litmus test would be an actual war. The rest is just chauvinistic trash talking so let's both try to avoid that. We can discuss these things if skirmishes and disputes actually escalate to full-scale war then we'll look into who claimed what and so forth.
India's issues with its two "antagonising" neighbours are mostly caused by British decisions during and before Indian Independence. Pakistan border issues will persist and there's no resolution anywhere in sight. Issue with China's borders are also mostly due to the British. Historically, pre Raj India didn't really have proper borders set up anyway, especially with China (I may be wrong on these because I'm no historian but do remember reading up on the sources of these issues) and China's borders in those regions were originally expanded to Tibet by Mongolian Yuan dynasty. It's these two large nation groups that began swallowing up previously undefined or poorly defined borders. There may be resolutions for China-India disputes but both are weary of each another at the moment. China thinks India wants to become a colonialist of sorts and maybe its leaders serving the interest of westerners. This thinking was set in the 60s. India has issue with China's support of Pakistan and thinks China's got sinister agendas and India's current BJP leaders are also part of the group (mostly western) that is thoroughly opposed to anything that has the word communist associated with it. Though the issues are less dire than Kashmir.
All three nations are nuclear powers so full-scale war is risky for the entire world. Being so close in proximity, it doesn't take much to wipe each other out. This means arms races and military build up for the purposes beyond defending from each other is quite pointless unless there are wide gaps between capabilities. For now, there is safety in MAD. China's worries honestly only lie to its east. Most of its efforts are focused on what the US has been doing and is planning. India being a growing market for Chinese products means China wants a stable and productive region but not one that is overly competitive against it. This means making sure no conflicts are started or get out of hand. The real race between China and India is therefore economic. Wealth brings improvements to life and overall progress of technology. To overcome each other's defenses, convincing technological superiority is of greatest importance. So because there isn't one at the moment, it is safe to say there won't be a fight anytime soon. But in a conventional war, China does have numbers and equipment advantage which would be recognised by almost all non-biased, well informed observers. The economic war waged on China today is a bigger threat to the country than any military force. You would probably be a person who encourages these things because you see China as an enemy. Not because it is a genuine threat to Indian self-determination (it isn't) but that's a convenient and comfortable line to think. Rather the real reason is because China has in fact been doing quite well and improved immensely over the last few decades. So much so that its new gain in economic and military power seems threatening and because it isn't Indian. That seems more likely as the source of bitterness Indians have for China, even more so than China's support of Pakistan and Chinese "Communism" (which hasn't touched India), or the border conflicts in the 60s which is also half India's responsibility as much as some like to think otherwise. So the real hatred grew out of frustration that China being an unfriendly nation to India has developed faster in a direction that afforded it greater military power to protect its interests.
