This is written in my personal capacity and follows from our report, which you can read here. I've ranked it in terms of importance and how easily one could make progress on solving these. 

1. Should China emerge victorious and seize control of Taiwan's semiconductor manufacturing capabilities and fabs, there are questions about the sustainability and economic viability of maintaining the operations of these fabs. Given the substantial costs involved in running the facilities and the toll of the conflict, would China find it prohibitive to continue these operations? And if they opt against it, what implications might this have for the pace of AI development?
2. In the event that Taiwan, while defending itself, chooses to scorch or sabotage its semiconductor facilities, the impact on AI progression would be significant. Questions about Taiwan's ability to rebuild and the reliance of AI labs on alternative chip suppliers like NVIDIA or AMD are something that one could look at.
3. How can we reduce the chances that China chooses to invade in the first place? Maybe we wouldn't have to concern ourselves with the takeover of the TSMC and other Taiwanese fabs if we could just prevent the PRC from invading. I've not read this but it maybe a good starting point. 
4. How long could Taiwan draw out a conflict? If they wish to boatlift their staff away from Taiwan to reduce the tacit knowledge available to the PRC, how long would this take, and can they do it in time? Again, mapping out war game scenarios could be helpful here. 
5. The extent of the US's commitment to safeguarding Taiwan's semiconductor stock is a matter of considerable interest. There have been some hints of a willingness from the US to destroy the Taiwanese fabs in the event of an invasion. What is the veracity of such claims, and what are the specifics of how this might be executed?
6. How quickly should we expect the potential advancement of Chinese AI capabilities, should they redirect Taiwanese chip production towards their own AI model training?
7. The extent to which a potential conflict between Taiwan and China might result in the destruction of Taiwanese semiconductor fabs as a byproduct of the war is also a matter of uncertainty. Something I'm imagining is that China chooses to bomb these fabs either on purpose or accidentally during a war. It's conceivable that China might regard such destruction as a regrettable, yet tolerable, consequence. Our report presupposes the preservation of these fabs at the start of an invasion, but the possibility of their destruction cannot be discounted. Our report assumes that these fabs would remain intact at the onset of an invasion. However, the reality that they could be destroyed during conflict by the PRC needs more looking into. 
8. There is considerable debate regarding China's military capacity to invade Taiwan successfully. A more comprehensive assessment or simulation of such a scenario would be invaluable in gauging the likelihood of a successful Chinese invasion. This might be the best work on mapping out how a conflict may occur, but I'd like to see more out there. 
9. A prevailing assumption, as discussed by others, is that China's threat to initiate a conflict over Taiwan stems not from a desire to control the 'semiconductor gold' within Taiwan but rather from a concern over global perception. Whilst this hypothesis aligns with my own intuition, I must confess a lack of certainty regarding this claim. It might be the case that the PRC doesn't care about the fabs in Taiwan, but to what extent is this true? It would be beneficial to have insights from someone with a better understanding of the Chinese context, offering a more nuanced perspective on this. Discerning this seems challenging and would involve having information that is probably kept secret.