(snipping ASBness)
1: How long will Taiwan last when China decides to invade?
2: Will it be long enough for the US to help?
3: How will this affect the Cold War this late into it?
4: Will this be enough for World War 3?
1. Depends. Is there a US CVBG in the area? If so, Taiwan will last for many years to come. If not, things
might get dicey.
2. Assuming a "no" on #1, almost certainly yes. Taiwan is hardly helpless, and opposed amphibious assaults are tough.
3. It probably won't.
4. No.
Even today, with the PLA's capabilities far in excess of the 1980's and the US much less capable, an invasion would be a tremendous risk at poor odds for little reward.
The PLA would need to establish air supremacy over the straight immediately (within 12 hours or less) and over all of Taiwan within 24 hours. Difficult to impossible.
The PLA would need to move a significant force of troops across the straight (by air or sea) and get them on the ground with at least some cohesion. Given air supremacy, possible but very hard and requiring a number of unconventional methods (merchant ship Trojan Horses, for example). Most of the troops sent ARE going to die.
The PLA would need to defeat Taiwan's ground forces QUICKLY. Given they can put troops ashore, possible but again tough and sure to ring up a high butcher's bill.
The PLA would need to convince the world that they were now the legitimate rulers of Taiwan and efforts to dislodge them aren't worth it. VERY hard, though a weak or sympathetic US POTUS would help greatly.
All this has to happen
fast, because once the US engages (which will happen within days) the odds of success plummet. A single CVBG can blockade Taiwan from any reinforcement or supplies. The US can easily maintain a blockade long enough to starve the PLA into surrender (the politics of which are messy, of course).
If China were assured of US neutrality somehow (which would mean at minimum the US is violating treaty obligations), the odds are
still not great, the expenditure will still be large, and the gain not very large.
Is there a chance they could pull it off? Sure. Better than, say, the odds of the Axis winning WWII? Also sure, because the political landscape is much more in their favor. However victory relies
absolutely on preventing any US involvement beyond the trivial, and isn't guaranteed even so.
Maybe if Taiwan was found to have the world's largest untapped reserves of platinum or something it might be worth it, but otherwise the cost/reward case just isn't there.
Edit: fixed a typo.