Some cultures use drugs for centuries (like khat) is "addiction" just a modern phenomenon? can addictive substances be used safely in other cultures?

Complex issue: There's nothing cultural about physiological addiction. It's real. What are considered "licit" vs "illicit" substances or practices varies widely by period & culture. Ditto for whether an addiction is accepted & accommodated by a society or condemned & persecuted. There is a very rich literature on this subject which is really more sociology than medicine. Check your library & bookstore.

Universal: Addiction occurs in every culture and every country. There is no safe place to use addictive substances. If you have a genetic predisposition to addiction, refrain completely. Remember, "No matter where you go, there you are." the image here is khat teeth. A detailed review of consequences of KHAT is available here http://apt.rcpsych.org/content/9/6/456.full

Varies with the drug: Addiction is not modern & occurs in all cultures, but the addictive potential of drugs varies widely. For example, tobacco & opiates are highly addictive for almost anyone who uses them, whereas most can use alcohol periodically without becoming addicted, but a moderate percentage have a genetic tendency to addiction. Others like marijuana & peyote have relatively low addiction rates. See comment:

No, it's not modern: Ancient medical texts from both the East and West have described problems with people with alcoholism and opioid dependency many thousands of years ago. Certain issues in modern culture, such as fragmented families, increasing stress, poverty, war, increased discretionary income in young people and other factors may increase the incidence/prevalence. But it has always been around.