Still, it could be done. I remember reading The Sum of All Fears by Tom Clancy - tldr; Islamic terrorists stumble onto an Israeli atomic bomb, kidnap a former East German nuclear engineer, build a machine shop in a cave, and rework the bomb into a thermonuclear fusion device. It seemed generally plausible - the science and engineering to produce a nuclear bomb is not exactly unknown, the biggest problem appears to be getting ahold of the right materials.
I watch the movie again once each few months. The movie has only a fission bomb. I have to suspect that building a successful, small fusion bomb would need quite a lot of computer simulation and also testing. The testing can't be hidden.
But a fission bomb could be plenty nasty.
You are correct: If can steal, say, a sufficient fissionable material, then might be able to do the rest without anyone noticing.
My understanding is that usually for a Pu bomb, have to compress the material like the US did with Fat Man. That compression is not easy to do. IIRC, there are some much more clever ways to do the compression, but, again, they would likely require a lot of computing and testing. That is, I'm not sure Pu would work in a gun barrel bomb.
I just know this stuff at the level of the two Richard Rhodes books and a few Wikipedia articles. I've never seen any classified material on bomb design.
It won't; it will predetonate, producing a "fizzle yield". With plutonium, the nuclear reaction starts so fast that the big problem is getting the critical assembly fully assembled before it blows itself apart.
With enriched uranium, the reaction starts so slowly that the gun bomb will work. That's why nuclear proliferation people are much more worried about enriched uranium than plutonium.
For a small bomb, would have to test it, and tough to do such tests without being detected.
Tough to be doing much with fissionable materials without being noticed.
Still, broadly, the OP seems correct -- nukes are dangerous.