I can provide information from the operational side of things, although I cannot say much about the engineering side of hanging a nuclear weapon on the belly of an aircraft.
The A7E was a US naval light attack bomber capable of carrying up to four nuclear bombs under its wing. The bombs it could carry were the B28, B57, and the B61. They were tactical nukes in the kiloton range. The A7E has been retired, but replaced the A4 in Vietnam, and then served as the light attack delivery platform for the US Navy until finally being replaced by the FA-18 in the mid to late 1980's.
The idea of using a kiloton range nuclear device over conventional bombs was described to me at one point. Let's say you are going to war, no, that you are seriously going to go to war, then when you hit an airfield you want to disable it. If you have limited assets it might be considered that using a tactical nuke is the best alternative. One bomb, one aircraft, and if they make it to the target, a hole in the runway that will not be fixed quickly, and of course all without the messiness of a megaton range bomb.
My experience with these payloads was as a loading officer and a delivery pilot. During my tenure at the squadron, which was 3 years, we only dropped one practice nuke, and this was done start-to-finish from the deck of the carrier. The A7E was loaded under the deck, brought up on the elevator, the pilot got in, took a catapult shot, delivered the bomb, and came back to take a three wire. By the way there were no "practice nukes," and every nuke we handled was the real one. It was a mindset.
Really, the only requirement that I saw from a loading officer or pilots perspective, was that you can hang the bomb under my wing. If you hung it, I could arm it. I do not remember any special cockpit procedures, except wear your eye patch. Other than that, you want the bomb on target, and so you want a platform that can deliver it, not too worried about it getting home though. Most bombing platforms today have that sort of technology. The point about arming is a good point, and I am not completely sure about my cockpit procedures. It was a long time ago, and anyway things have changed. My guess is that there were no special arming requirements, a pulse of electricity was delivered to the station under the wing, which activated the release. No other bombs had any special arming considerations. Essentially, a charge was initiated and a boot kicked the ordinance off the wing.
Why can some tactical jets carry such a weapon and others can't? I am not sure about this, but some of the considerations are payload weight and physical constraints of the delivery aircraft, e.g. wing size, bomb bay size, etc. There are also characteristics of the bomb as it departs the aircraft. If it has aerodynamic modes (because it is flying) where it comes back up to the aircraft and collides then it will not be allowed under the wing. So I would speculate it has more to do with airframe aerodynamics and physical constraints, and less to do with electronics and arming.
I also was on the standing mission planning team aboard the ship that considered the strategic and tactical issues the pilot would face in a given delivery. Don't want to talk about the sort of intelligence we were given to make our decisions. There wasn't any thing out of the ordinary for the mission planning folder that would be handed to the pilot when the time came. Just a bombing mission planned in advance and reviewed by the upper echelon.
I will make this comment. In the A7E we were given a packet which included a kneeboard chart, the navigation charts for the low level, and an eye patch. Don't remember much else in it that concerned me. The chart gave me the path in, the path out, and the location of the carrier to come back to. We always joked about coming back to the carrier, as if it was going to be where it said it was. Also we had ways of entering the airspace of the ship without radio communications so you wouldn't get shot down as a threat. That too worried us as pilots. But the eye patch? So I asked about that. Here is what I was told:
Your route to target will be deconflicted with other targets, i.e.
other tactical nukes going off at different locations and times in
your forward hemisphere before your own delivery. On the chance that
one does goes off at the wrong time we have provided you with an eye
patch. Put the eye patch on before feet dry, and if you find yourself
blind, take it off and fly with the redundant eye to your target and
deliver your weapon. See you when you get home.
Okay. I get it, we are really serious about this! This brings up the last point I wanted to make. We always delivered our nukes in a manner that was different than conventional bombs. It was about getting away from the blast zone as quickly as possible, and in particular the electro-magnetic pulse, which would render us virtually helpless. The electronic fuel transfer switches would be fried and the available fuel left in the various tanks wouldn't get you very far. Not to mention all the navigation systems and such that would be inoperable. At the time I was flying missions we used the loft and the laydown deliveries, which purportedly allowed us to survive the detonation. The loft was at 3 miles, pull up into an Immelman with 1 G. After completing the Immelman depart back to the ship. The laydown was delivered at 200 to 500 feet, above the power lines crisscrossing a country, as fast as you could go, with an exit straight away from the target. Still, that fast and low, hard to see the target. This helps to isolate you from threats inbound and outbound. Each delivery had its benefits and risks.