I'm not a doctor, so this is just based on my experience taking it and my knowledge being a healthcare professional....but I hope this helps a little.
-It does not typically cause insomnia and anxiety. I never noticed this.

-The hypomania could be that your BP symptoms are "leaking through" the meds. Lamictal is shown to be more effective in preventing full-blown episodes rather than treating acute mania or hypomania when used as monotherapy. A few of my add-on meds with the Lamictal helped wipe out some of the residual symptoms and did not give me side effects. I'm not on stabilizers like Depakote or Lithium due to Lamictal having less side effects for me.
-I do believe insomnia and anxiety can possibly be withdrawal affects from the antidepressant. I absolutely experienced this.
-As far as your last question, the rash usually occurs in the beginning of treatment or when you aren't tapering up correctly. If you've been on it for a little while and the rash did not occur, then you are more likely to be someone who will never get the rash. However, this does not mean Lamictal is right for you. Maybe give it time?