Can your spouse naturalize? If yes, you may not have to leave the US but you should consult with an attorney regarding your options.
Yes you can change status from H4 to J1 in the US. For J-1 exchange program, you have to be sponsored, and you cannot self-petition. You should seek the advice of an attorney.
You should also have with you the I-131 receipt notice and biometrics notice to show you filed for a re-entry permit and did fingerprinting prior to leaving the U.S. As my colleagues recommended, you should consult with an immigration attorney prior to entering.
They will most likely ask you about the arrest, but I doubt that they will ask about the taxes from the 90's unless you checked the box that you have not filed taxes. You should bring copies of your last 3 years tax returns and if you owe any money to IRS, you should bring evidence of payment plan. If you are worried, you should consider consulting with an experiencing attorney and hiring one to attend the interview with you.
As of November 12, 2014, NVC is no longer collecting original documents, so a good copy will suffice.
You don't provide enough information. Do you have a green card application still pending? You should consult with an attorney to advise you of the next steps, if any.
You should consult with an immigration attorney immediately. A false claim to US citizenship can have very dire and sometimes permanent consequences.
If you are in O-1 status as an alien of extraordinary ability, there's is the EB-1 alien of extraordinary ability category for permanent residence. Although it's called the same, you will need to submit substantial evidence that you meet the criteria. These petitions can be difficult and you should consult with an immigration attorney to make sure you are eligible, chance of success, etc.
You can check either or both if it applies to your particular situation, and you must submit all the proper evidence of your good faith marriage and/or extreme cruelty. You should probably consult with an experienced immigration attorney who can help and guide you through the process.
You should not leave the US, otherwise, your I-539 will be deemed abandoned.