Because of declining birthrates, Muslims could eventually gain a majority in some EU countries............
1) Can these countries opt out of a democratic form of government and institute Sharia Law by popular vote, much the same as Hitler was voted into power and then immediately got rid of all democratic institutions?
2) Once these countries accept Sharia Law and therefore inherit all the infrastructure of the former country, such as nuclear bombs and missles, can they then declare war on the US and target us?
IMO the US needs to implement a national NMD at the earliest possible opportunity.
This question assumes that the current forms of government in Western Europe would continue to function as before even as the Islamic population grew closer to the tipping point.
I think it more likely that countries at risk of turning Islamic, such as Belgium and France, would likely become ungovernable as currently constituted once Islamic immigrants form the majority of their urban population, but before forming the majority of the overall population.
These countries would likely break apart into Islamic-controlled city-states and xenophobic European-controlled successor states.
2) Once these countries accept Sharia Law and therefore inherit all the infrastructure of the former country, such as nuclear bombs and missles, can they then declare war on the US and target us?
Again, this assumes that these countries would continue to exist as currently constituted up to the moment Islam takes over, and that the minority European populations would peacefully submit to their new rulers and turn over the infrastructure to them without protest.
I think it more likely that much of these countries' wealth would be transferred out of the country to safer havens before an Islamic takeover. Not just personal assets, but also corporations moving their headquarters and manufacturing plants offshore.
I also think that a lot of military infrastructure would either be destroyed in combat in civil war or deliberately to keep it out of Islamic hands and turned on the Europeans.
The Islamic countries would inherit a scorched earth Europe with significant European populations which, for sheer size, would take much effort to suppress. Attacks on the United States would have to wait until the conquered territories of Western Europe were pacified and reorganized internally along Islamic lines.