Yes. Color vision is not an issue with driver's licensing. All traffic signals are made of colors that will not be confusing to the color deficient . Driver's license testing only is concerned with line acuity (like 20/20) and field of vision (how far can you see to each side).
Yes. Most states do not test for color vision to get a drivers license.
Depends. The most common type of "color blindness" is red-green color deficiency. Blue-yellow deficiency or true color blindness (achromatopsia) are rare. Color testing can identify which. The problem is a lack of certain types of cones or their opsins (light-sensitive compounds). Red-green deficiency can be adapted to fairly easily and is not very limiting, but the others can significantly impact vision.