Nanotech seems to be smaller risk than AI or biotech, but it advanced form has many ways of omnicide. Nanotech will be probably created after strong biotech, but short before strong AI (or by AI), so the period of vulnerability is rather short. Anyway nanotech has different stages it its future development, mostly dependent on its level of miniaturisation and ability to replicate. To control it in the future will be build some kind of protection shield which may have its own failure modes.
The main reading about the risk is Freitas's article "Some limits to global ecophagy by biovorous nanoreplicators" and "Nanoshield".
Some integration between bio and nanotech has already started in the form of DNA-origami. So may be first nanobots will be bionanobots, like upgraded version of E.coli.
Pdf is here: http://immortality-roadmap.com/nanorisk.pdf
1) I think that the reason there were early fears about strong nanotech was a lack of appreciation at the time of how hard it is to work at that scale. Things stick to each other, either move extremely slowly or extremely quickly, and you can't see what you're doing. Feynman, say, had this completely off-the-wall suggestion for making stuff on the nano-scale based on scaling machinery down further and further. By the time I was reading it, it was laughable. Maybe it was laughable at the time, but it was certainly possible to think that.
3) DNA origami on nanoparticles, even combined with modified bacteria, doesn't seem like the kind of thing that's fundamentally capable of gray-goo-ing. Certainly not the kind of gray-goo-ing that we can't do anything about.
1) I think that bionano field of combining living cells and DNA-origami would solve all this problems.
3) Grey goo is mostly obsolete risk, but nanoweapons still real. Something that gets from bio the ability to replicate in environment and from nano the ability to execute right program in right pace.