Sounds like there wasn't enough drywall compound or topping compound used to fill all the voids. If you're seeing every fastener, there are likely many seams that are equally hollow that will cause shadows and be apparent no matter how much paint is applied. As for being able to see yellow streaks and ink lines, then it is equally likely that no primer was used and both inexpensive paint and not enough paint was applied to adequately cover and hide.
Patches are made on painted walls all the time without sanding off the paint first. You shouldn't have to sand anything before applying more topping compound to the fasteners. I'd also check for hollow seams and fill them as necessary. Once all that is done, if the walls are textured, I'd recommend floating the walls smooth and retexturing from scratch. The reason for this is that trying to blend in dozens of 3" dots on the wall will be next to impossible, add a couple seams to the dots and you'll have a terrible looking wall. By floating it smooth, you're starting with a clean slate and will be much happier with the end results.
If the marks are indeed pen, they will continue to bleed through. Use a stain blocking primer such as Kilz or Zinnser 123, two good, even coats. Follow that with two good, even coats of a good quality paint, such as Kelly Moore or Sherwin Williams, two of many good brands.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!