How long do young adults have major depressive episodes for?

Depends on treatment. With appropriate treatment, depressive episodes can be cut short. Cognitive Behavior Therapy and antidepressant medications are effective in successfully treating depression. Generally, the sooner one is treated the shorter the episode.
Varies, at least 2wks. To qualify for the diagnosis of major depression, the symptoms of concern must last at least 2wks, they can last as long as to become chronic.
Varies. Some adults have a single episode of major depression that lasts 2 weeks to several months, and never have one again. In others, the first episode of major depression is a prelude to a lifelong struggle with recurrent depression. In general, the stronger your family history of depression is and the more episodes of depression you've had, the more likely it is that you will have future episodes.

Related Questions

I was diagnosed with dysthemia w/major depressive episodes. My psych suggested a neurologist. Why and what could the findings be?

Other things. Your psychiatrist may think that you have some organic cause of your mental problems. See the neurologist.
Mood and neurologist. The simplest thing to do is ask your psychiatrist or psychologist speculation and assumption is simply going to make you more worried and cause more anxiety and more frustration. If your relationship is good with your psychologist and or psychiatrist simply asking why did he referred you to a neurologist. So to give you a differential diagnosis of all the possible diseases is not a good thing here.
Ask Your Doctor. Your doctor is the best person to answer your question. It is likely that he/she wanted to make sure that you don't have an obvious neurological reason for your mood related problems.
I would ask. Your pyschiatrist since they recommended you see a neurologist. I would guess (note I say guess) that they are just worried that you might have a brain tumor or some other condition that is contributing to your derpression.

I have long periods (6-10 weeks) of depressive episodes, followed by small periods (1-2 weeks) of hyperproductivity, lack of sleep, cheerfulness?

Mood disorder? We all get depressed but the cycle you describe might be a mood disorder. Please talk to your doc or a mental health professional. Help is available if needed. Peace and good health.
Agree w Dr. Seif. It is important to have this evaluated to determine if you have a mood disorder. Rule out unipolar or bipolar depression.