For the screen, try a small amount of WD-40, sprayed onto a soft cloth. (This issue comes up from time to time, and this solution usually helps although YMMV.)
Using an abrasive on your screen? Hmmm, probably not the best plan of action. I'd use rubbing alcohol personally. It'll remove the ink from the sharpie easily.
Go to an office supply store and purchase a couple of items: graffiti remover/marker remover for white boards, and white board cleaner.
Secondly, I would see if the same store sells microfibre cleaning cloth and use that cloth for cleaning your screen while using these items. If the store doesn't have it, just go by an automotive store and ask for a "detailer's cloth" which typically is microfibre. Finally, if that doesn't work go by an optometrist and purchase a lens cleaning cloth.
I would first apply the whiteboard cleaner to the cloth, then experiment on an out-of-the-way corner, just to make sure the material and cloth is safe on your screen. I'm sure it would be. Then venture to the permanent marker area and work with that.
If the white board cleaner doesn't work, then get the graffiti remover and give a try with it. Experiement in a screen corner first.
Hopefully, this will work and you are not using anything that is abrasive, also these chemicals are known to work well and safely with plastics but I would still work with a corner first, as a test.
Per its web site; the Mr. Clean Magic Eraser is "[n]ot recommended for the following surfaces: High Gloss, Polished, Dark, Brushed, Satin, Faux, Bare/Polished Wood, or Stainless Steel."
Isn't the MacBook's screen glossy?
I would stick with the tried and true advice of Tuttle and Joe and steer clear of Mr. Clean.
Although the special properties of Basotect® represent a genuine advance in mechanical cleaning: the apparently magical powers of the Mr. Clean Magic Eraser, like many other methods, are based to a great extent on the principle of abrasion in which stubbornly adhering dirt is removed mechanically from the surface to be cleaned.