Very simply, static electricity is caused when certain things rub together. Try this easy to understand explanation by Ron Kurtus in Milwaukee, WI.
The way electric impulses work in nerves is not the same as the way it works in wires, or in static electricity. The nerve impulse is carried by a change in electrical potential represented by a difference in the concentration of ions across the length of a nerve axon membrane. Typical ions are Ca++ or Cl- ions. It's not so much a flow of electrons as happens in an electric wire, rather it is a flow of electrical potential. In that way it's quite different than electrical conduction of a wire or a circuit. Check out this explanation of how nerves work (under "Neurobiology").
It is possible to increase brain activity, but this is usually done with drugs or chemicals and should only be done with medical supervision. Damage can occur depending on how much drug (e.g. alcohol, or amphetamine) is used.
Bipolar disorder does not have anything to do with the polarity of electrical things like the plus and minus of electric charges. The two "poles" in bipolar disorder are Manic and Depressed states of mind. There is absolutely no correlation to electricity or electronic theory. Frankly, there's a lot of speculation, but scientists have very little idea what causes bipolar disorder. There are many vague theories but there is no definitive cause known for this condition. Terms such as "hypothesis" and "theory" abound. Unfortunately, in answer to your last question, the bottom line is: we don't know.