Can you take painkillers when getting a tattoo?

Sure. Pain killers should be fine. Tylenol (acetaminophen) is better than nsaids (aspirin, ibuprofen) as they can increase the risk of bleeding slightly. However, ice is even better for pain and swelling so that's where i'd start.
Yes. You can. If you are concerned about having enough pain to require a "pain killer" maybe you need to rethink getting the "ink".
Yes. If you are already on pain killers for a chronic condition there is no reason to stop them, however i would not advocate "upping" your dosage without consent of your prescribing physician. Keep in mind, "pain killers" have a potential to lead to chemical dependence, in that light i would not advocate obtaining pain killers specifically for tattoo placement. Tylenol (acetaminophen) or Ibuprofen should be adequat.
Yes, but... If you are having pain, tylenol (acetaminophen) or Motrin can help (use with label instructions), though these would work best for afterward. I do not recommend taking norco, vicodin, etc., since these have major side-effects when not used appropriately. However, if you are worried about the pain, perhaps you should reconsider your need and reasons for the tattoo.