There is believed to be a software remote disable in the ASML provided machinery but it doesn't have to be effective - an invasion would cut off the machines from the maintenance they require https://www.theregister.com/2024/05/21/asml_kill_switch/
It's completely speculative for us, but I'd point out only the US has incentive to do that, not Taiwan. The only reason Taiwan would do it is if they adopted a scorched earth policy like Saddam and the burning Kuwaiti oil fields. But even with a psychopathic dictator like Saddam, he never burned his own oil fields.
Not even necessary. The equipment will cease to function if it is cut off from ASML servers in the Netherlands. But yes, a destruction protocol exists for most strategic resources located near adversaries that are considered critical to national security.
Weapons systems and strategic production capabilities are the one area where I think that DRM actually makes sense. Not printer cartridges and coffee. FFS.