WX Man
In your first question.
Rain ice is a unique airframe icing. Rain must be produced from a layer of warmer air. This rain must then fall into an airmass where the temperature is below zero. As a result these rain size drops will eventually become supercooled. Now, if that airmass is very very very cold then the drops will become super cooled very quickly indeed. AND your aircraft will be flippin cold too.
If that airmass is not so cold, the drops may take a while to freeze and become supercooled.
Your theory is right but for Rime and Clear ice, not for Rain Ice or Freezing rain. Closer to 0°C the larger the droplet.
Question 2.
The question is asking for a TRIGGER.
These are the conditions needed for a thunderstorm.
1) Unstable atmosphere (steep/high ELR)
2) Moisture
3) Trigger action, these are
a) Convergence
b) Convection
c) Orography
d) Frontal
Hope this helps. Obviously, CONVERGENCE IS THE ANSWER
By the way convergene and stability have no relation to each other what so ever.
Your third question
I agree with you. But, instrumentation was never my favourite. This isn't really a "met" question, so I'll bow out.
Hope this helps
Steve Francis