If a ship carrying R2 is ionized, does the R2 unit make the mandatory white 1 straight maneuver the next turn a green 1 straight maneuver?
R2 and Ionization
Yes it does, page 12 of the FAQ 
Yes, as mentioned in the FAQ.
If a ship carrying R2 is ionized, does the R2 unit make the mandatory white 1 straight maneuver the next turn a green 1 straight maneuver?
The FAQ is a powerful ally, young padawan. Learn all you can from it. 
Just go FAQ yourself. You'll thank us later.
Nien Nunb works the same way as well.