In a full cold war scenario the following article predicts Australia’s export income would fall 55%.
An actual kinetic conflict would leave Australia with the hard choice of breaking ties with the USA or face an economic depression.
Japan and South Korea would have a worst choice as they are within range of a lot more ordinance than Australia. There are probably only a few targets is Australia worth the class of ordinance that would be required to strike them at such distance.
India may help from the side lines but not to the level they get drawn into actually fighting. They are not going to open a second front in the Himalayas. I doubt India would ever risk a war with China as long as Pakistan and China are close.
South Korea would like to disappear from the whole show. North Korea close with China is a big threat against being involved in any war against China. Just about every under ground car park in Soul has an bomb shelter sign above the entrance. I dont know if it's a coincidence that the Soul's largest mall near the center of the city is under several blocks square with 4 or 5 shopping levels under ground. South Korea would keep the status quo with USA forces stationed in South Korea. I wouldn't be surprised if they demanded any forces currently based in Korea that the USA wished to deploy against China would have to return to the USA before deployment to Japan/Guam etc
UK if the Torries are in power hell yeah, other wise maybe some logistics or some vietnam era ballsie hell no
Japan current politics and for the foreseeable future the USA would undoubtedly be able to use it bases in Japan. Whether the JSDF participated in kinetics would depend on what politic spin could be applied, it might be hard spin joining the USA against China because China attacked Taiwan. However preemptive attacks by China on US naval bases, especially ones in Japan would almost gaurentee the JSDF playing an active part.
I think it is highly unlikely China will strike the US forces as part of AR. China unless cornered is not going for AR unless it knows it is the dominate force against the assets the USA could muster.
If the USA and friends would just stop picking the scab of the wound that is the Taiwan issue, eventually it will heal and Taiwan will be assimilated into China