I'm quoting Thaddeus in the question you linked :
Under a red sun, he appeared to be Human in all the ways that mattered.
Thus, the answers :
- He could be affected by any drugs.
- He could be addicted to any drugs.
- You say it is "quite hard for a common person to conquer the addiction by his/her own will". Superman is no common person. So I guess he could, even if it would be hard.
Not really much more to say, since the details are in the question you linked. Maybe one more thing : if Superman was addicted to a drug under a red sun, I suppose as soon as he would get under a yellow one, the addiction (chemical dependency) and effects of the drug would fade instantly.
EDIT after the comments : I really think he would instantly lose the psychological addiction too. Drug is not like a gambling problem. There should be a question about this kind of psychological addiction though :D. So, the addiction to drug stems from chemical processes. Those processes would fade. And Supe wouldn't be able to get those effects again. Smoking or injecting something (provided you manage to inject him something...) would have the same (if not less) effect than a glass of water on a human... I'm not that fluent in english so I don't understand in the Wikipedia article if Cold Turkey has biological or psychological origins. Feel free to edit.