The US has a one-china policy so we kind of already acknowledge that Taiwan is part of China.
Yes, and no. People should know that we "unofficially" recognize Taiwan, and actually still have a defense treaty with them.
First is the unusual status is that although we do not have an embassy there, we do have the American Institute in Taiwan, which fulfills the same purpose. And Taiwan has a similar operation in the US, the Taipei Economic and Cultural Representative Office.
Then there is also the Taiwan Relations Act, which even calls for the US to respond to any threat against Taiwan with force. That was enacted by President Carter at the same time he ended the "Two China Policy", and remains in effect to this day and all presidents after him have also affirmed their commitment to that.
So no, we have not "acknowledges" that Taiwan is part of China. Quite the opposite actually. We have affirmed they are independent and will remain so unless they decide otherwise. And any actions against them will be met with force.
Geography dictates that the US would lose that war anyway without using nukes. China already has enough missiles to be able to drive the US Navy back off being able to do much without China even launching its first boat. Taiwan is well within reach of china's mainland missile batteries.
Actually, geography dictates nothing of the sort. And the number of missiles means nothing, they would have to find the Navy first. And that is much harder than you apparently think.
Yes, Taiwan is within range. Then again, it is an island and nothing on that island is moving. Shops at sea are something completely different. And apparently you are seriously overestimating the effect of those missiles. Are you even aware that during WWII, Germany fired over 3,500 rockets and missiles at England? Do you think that destroyed them?
So far, Russia has fired over 5,000 rockets and missiles at Ukraine. So they seem like they are out of the fight?
Why people seem to believe just a few rockets or missiles will end a war is completely beyond me. That has never been the case, is not the case now, and will never be the case in the future. It honestly blows my mind that some people are so absolutely simplistic in their thinking of how effective missiles actually are. Almost like they are magic weapons from the Harry Potter universe.