Is there any proof bipolar disorder is a chemical imbalance in brain?

Yes: There are a lot of different pieces of evidence supporting the argument for a "chemical imbalance". You sound skeptical, and i will try to not be too technical. A piece of evidence is family history, if it was not mediated by neurochemicals then why would one identical twin be more likely to get it if the other has it? You may want to google "pubmed pmid: 23371914" and read how lithium may work.

Not clearly: Noone knows exactly what causes bipolar disorder, but we do have evidence showing that extreme mood episodes like that in bipolar disorder must be from chemical imbalance as often medications that readjust these chemical balances between neurotransmitters like dopamine, serotonin, norepinephrine etc work effectively for the disorder.