Ask about all pensions, retirement accounts, debts owed to that spouse, stock options, bonds, and life insurance. You are entitled to half of these assets, though they are often forgotten in "discovery".
The chosen questions at your divorce deposition should be deferred to your attorney who already has a background on the situation and your personal circumstances.
During divorce deposition you should ask all questions that will give you information relevant to all aspects of your case. Both parties have to give answers under the secrecy oath.
Usally the judge decides what needs to be taken care of by state law. Just make sure all assets, division of personal items, child support, martial debt, and allimony issues are discussed and agreed upon.