Yes. As long as your field of vision and visual acuity with one eye is still within the legal range. You would have to turn your head to look more, and know that depth perception would be off (need to adjust to monocular cues).
Maybe. An eye patch will most definitely cure double vision caused by eye misalignment (binocular diplopia) but raises other issues regarding visual field and depth perception. Most municipalities allow driving with only one eye - check locally and do what you feel safe with. Hopefully, the problem is only temporary.
Dominant Eye. If you have a dominant eye, that would be the most logical choice. Please be careful as driving with monoccular vision can be challenging if you are not used to it.
The affected eye. You should patch the eye that has been affected by double vision., ie., the one that doesn't have full range of motion.
Use on strong eye. Patching is aimed at strengthening the weaker eye. Therefor cover the stronger eye. However be very careful because you will lose peripheral vision and depth perception when you use a patch. Discuss this with your eye doctor.
Very dangerous. By wearing a patch on an eye (either) you create a potentially hazardous situation if you were to also drive. I agree that patching the best eye is the way to strengthen the weaker one, however, I don't believe anybody should be driving under those conditions. I believe for your safety and the safety of the public you should refrain from driving until you no longer need the patch.
Cover right. Most hazards that are important in our society where we drive on the right side of the road, come from the left. So you need the peripheral vision of the left side, so cover your right eye for this purpose.