Do people with narcotic abuse have a lot of pain?

Yes. Paradoxically, patients using narcotics chronically have more pain when they are injured.
Yes. People who abuse opioids chronically may suffer from generalized pain if they wait too long between doses, even if started without any pain. It's a withdrawal symptom. The need for higher doses over time is called tolerance. Addiction is more about trying to prevent withdrawal than getting high.
Some do. The concept if opioid induced hyperalgesia exists. This means that those taking high dose opioids can be extra sensitive to painful stimuli.