My father died of a heroin addiction, will I get addicted to narcotic pain killers more easily?

Good chance. 1/3 of people exposed to opiates develop an opiate addiction. Studies found approximately 40–60% of the risk of developing an addiction to heroin is genetically determined. These genes though only connote broad complex personality and physiological traits like impulsivity, risk taking and stress reaction-a vulnerability to addiction- not a doom. Fair warning; be safe. Always let prescriber know.
No. It is a choice - so choose your habits carefully; if you know hurting a person can put you in jail and you have not hurt anyone yet - then you would not be addicted either since you have the awareness of what havoc it causes. Addiction is a response to inner pain so deal with your emotions by joining a support group.