Ok, I am trying this without much actual aviation-knowledge, but have been encouraged that this is not out of scope (I actually have no clear idea where IRF-regulations start and end... I know what a dragon looks like, though ^^).
As thisthis answer points out, dragons will most likely not require instruments to see. But they will be safer if SEEN. collision-avoidance would most likely be mainly for the dragons to manage, because they just have an easier time manoeuvring, but for IRF for pilots, it would be helpful if Dragon got Transponders to signal their position.
About weather-minimums: It really would fully depend on the dragons again. They may avoid flying in thunderstorms naturally, and at the same time be perfectly content to start, fly, and land in the middle of the most terrible blizzard... perhaps they just don't get cold, but lightening is an actual danger.
Winds are just as dragon-dependent: if they have capabilities for in-storm-flight like, say, an Albatross, even a strong hurricane may not keep them down.
In bad enough conditions, they may actually have the airspace to themselves!
About what they may sound like to ATC: This is Dragon 101, I am patiently flapping my wings above your tower, may I please land on it until you have the metal-tubes sorted out?
A bit more serious: I would not imagine them much different from normal ATC-talk, just perhaps a bit impatient with those clumsy humans :).
Something that just came to mind about flight plans: we have airways defined for airplanes anyway. Would dragons OUTSIDE these airways be regulated at all? If not, the problem may actually be reduced to having controls in place for "crossing the street" and "I want to land near the airport, please". Dragons purely amongst themselves pose a lot fewer problems that dragons and airplanes.
