Yes and no. The class may stay on there, but the repeat would probably be counted in the GPA, not the W. Chances are pretty good that the repeated class will be noted though and not drop off the transcript entirely. I would suggest reading the school's policy about dropping/withdrawing and repeating classes. It should be in your student handbook or catalog of classes, somewhere in the administrative stuff near their grading policy.
Yes & no. Some schools will get rid of the W if you re-take the course within a certain time frame. Other schools keep the W on your transcript. The W doesn't count against you in your GPA calculation.
You can see at the bottom of your transcript "credits attempted" vs. "credit earned". You'll see a difference in these totals if you have a W on your transcript. Typically, your GPA is calculated based on quality points. Take number of credits in a course and multiply by grade received. This equals the number of quality points. You divide the total number of quality points by total credits earned to get your GPA.
If you've attended more than one school, you'll need to add up all the quality points and all the credits earned from each school to get your cumulative GPA. This can get a bit hairy if you have one school on semester hours, another on quarter hours and another on trimester hours