There are four ways to deliver nukes. By intercontinental missile, by sub-launched missile, by aircraft dropped bomb, and by ground transported and detonated. Each presents their own unique challenges for defense. Bombers are not a huge threat. They are slow and easy to see coming due to their logistical footprint. Traditional air defense, so long as it is intact, can defend against that. This is why bombers are the last wave of nuclear attack; the first two waves, ICBMs and nuclear subs, target silos and air bases first. Nuclear subs are powerful because they get in close and are very difficult to track. They present a big question mark in a country's nuclear ability and are a major component in the "protection" of Mutually Assured Destruction. To defend against them, you have a myriad of sub detection techniques and hunter-killer subs. Post-launch, the missiles are defended against in the same ways as ICBMs, which I'll get to next. ICBMs are an interesting variable. They are stationary, and it's pretty hard to hide the construction of a twenty story hole in the ground from ground and satellite observation, thus it's safe to assume that other peer countries know where each other's silos are. Protection, as far as public knowledge of US systems goes, is three fold. Aegis missile cruisers, if close enough, can destroy the first and second stage missile bodies, before the nuke goes sub-orbital. The third level involves taking out the warheads post re-entry with Patriot missiles, but there's a very narrow margin of time. Those warheads do re-enter at mach 20+. Thus the U.S. developed the THAD missile system. It's a crazy powerful intercept missile that kinematically - by means of physical impact with - defeats the re-entry vehicle as it re-enters. It's pretty cool. A lot of that depends on detecting launches, thus the US has ask sorts of satellites to detect them. Some have their own orbits, others are piggy backed on other satellites, like the US's GPS satellites. They are designed to detect the massive UV spikes of rocket thrust or other telltale signs. Ground based donations, such as smuggled in nukes, present the largest threat, in my opinion. You have to detect the radioactive body or threat communications. While other nukes would target military, maybe industrial, targets, these types would almost certainly target population centers, as they are more likely to be used by those who want to fight a war of ideology against a people, not a government.

No. We've signed treaties that prohibit us from militarization space. Beyond that, the physics makes it pretty difficult to efficiently do it anyways.