Thats an easy one. Physical hardline from the bomb to an external antenna / cell phone. And if you can build the infrastructure to produce a functional nuclear weapon, you can probably figure out a simple remote relay switch. One would hope anyways.
Sure. Of course, the contents of your shipping crate are looking more and more obviously like a bomb at that point, but I'll grant that there are certainly ways to do this.
Depends on where in the stack it ends up, with larger ships holding up to 14k containers you can likely hide phone easily even on the outside, There is plenty of spaces on a container a small phone could be hid and not noticed unless inspected closely.