What effects can I expect if I go off an antidepressant & start taking a mood stabilizer for bipolar II disorder, but I am really not bipolar?

Antidepresant effect. Some mood stabilzers actually have some degree of antideressant effect. In fact, some of these meds are used to treat non-bipolar depression, such as abilify. Lithium is sometimes used as an add on for treatement resistant depression. Other meds used as mood stabilizers may have antidepresant effect , such as geodon, (ziprasidone) seroquel, Lamictal and others.
Good question. If you are not bipolar, mood stabilizing meds are unlikely to be effective in elevating depressed mood. They may help in stabilizing other traits that are common in bipolar but also otherwise, for example. Irritability. Antidepressants are not a great idea in bipolar depression because they can trigger manic or hypomanic states. In fact, that's one of the ways that bipolar makes itself known.
It depends. If you come off the antidepressant correctly, you should have very few side effects. Make sure you discuss cessation/transition of medicine with your physician. If you stop the antidepressant suddenly, you could have symptoms that range from nausea, anxiousness or headache.