Serious symptoms. "melancholia" is a subtype of major depression. The person has severe vegetative signs: loss of energy, loss of appetite, motor slowing or agitation, and insomnia -- as well as feeling much worse in the morning. Medication can really help these signs of melancholia, along with the cognitive and affective signs of depression. A psychiatrist can evaluate you & make helpful recommendations.
Depression. Possible but not easy, through insight-oriented psychotherapy and group therapy for added support.
Sometimes. Start with talking therapy (such as cognitive behavioral therapy or insight oriented psychotherapy). Don't isolate. Spend time w people. Having a support system is very important. Get out. Don’t allow yourself to stagnate at home. Work to get at least 8 hours of sleep per night & eat as healthfully as possible. Daily aerobic physical activity is a big +. Try acupuncture, tai chi, qi gong, yoga >.
Possible, but... It's hard work. Many (but not all) people with depression can be helped if they did certain things irrespective of feeling down, depressed and unmotivated, including specifically, increasing their socialization, avoiding alcohol and substances of abuse and doing 30-45 minutes of aerobic exercise 5 days a week. When the depression is severe, avoiding antidepressants might be counterproductive.