Can a person who has diplopia see clearly?

Yes and no. Diplopia means that the brain cannot fuse the dissimilar images it is receiving from eyes looking in different directions. Usually the vision in either eye is good, but only made unusable due to the double image.
Usually but . . Someone with diplopia, and normal eyes can see clearly. Each image will be clear although the doubling is confusing and not tolerable. Some have diplopia with one image being blurry and these folks can sometimes ignore the second image.
Depends. Is dependent on the degree of diplopia and the individual eye's visual acuity. Severe large angle diplopia is disabling, and one eye has to be covered to see better. Smaller diplopia can be corrected or sometimes just ignored depending on how constant it is.