Unlikely, as those flights would be scheduled and the launch site publicized. It wouldn't absolutely preclude a masked nuclear strike, but that would be possible already with space launches.

It'd also be a pretty shitty first strike, since you'd be limited to the count of starships scheduled to launch (and likely only ones headed generally in the direction of your target if you really want to mask it) at about the same time. So, probably just one or two, at best. Meanwhile, you'd need at least dozens (of missiles—more warheads) to have any hope of substantially reducing a major nuke-armed opponent's capability to retaliate.

Not remotely worth the complexity of setting up and executing. Maybe worth it against an opponent with extremely limited launch capacity (North Korea?) but that's a pretty niche application.

Until we have some magical non-polluting rocket fuel, I can't imagine intra-planetary rocket trips ever becoming permissible. Planes are bad enough.

Ignoring production, hydrolox would work, not that spacex are going down that road

Oh interesting! Rocket science is cool.