Often together. The 2 of these often come together. "addiction" signifies a behavioral pattern of using a substance despite obvious harm to the person's life, work, and relationships. They use more than intended; lie about using; and spend lots of time using it. Physical habituation (having withdrawal symptoms when missing dose) can happen without addiction, but may come with mental/behavioral patterns as above.
No difference. All addictions are both mental and physical.
The line is blury. In a classical (physical) addiction the body changes by creating more receptor sites for the drug to which you get addicted. In a mental (emotional) addiction you find the drug/experience pleasurable and want to repeat it. Basically both feel the same to the individual and both are difficult to break.