A clear answer is going to be hard to find. Your situation is complicated and requires expertise in 2 states. Here's my shot (I'm not specifically knowledgeable on NJ or MD):
Q1. If we file federal jointly, are we allowed to use married filing separately for NJ and MD?
A1. Yes for MD, "yes, but" for NJ.
https://www.rosenbergmartin-tax.com/news/to-file-jointly-or-separately-considerations-for-married-co...
"In most cases, if you are married and file a joint Federal return with your spouse, you must file a joint New Jersey return." "Nonresidents: If both you and your spouse were nonresidents of New Jersey during the entire taxable year, and only one of you earned, received, ore acquired income from New Jersey sources, the spouse who had income from New Jersey sources may file a separate New Jersey return (Form NJ-1040NR), even though you filed a joint Federal return. You have the option of filing a joint return, but if you do, joint income must be shown on your nonresident return"
https://www.state.nj.us/treasury/taxation/pdf/pubs/tgi-ee/prior_years/git4_1203.pdf
Q2. As I have a MD license and voting address, am I liable for taxes in Maryland?
A2. Yes see Q/A 4
Q3. If we use married filing jointly in NJ, will my spouse's income be taxable in NJ (not from NJ source)?
A3. No. You have to allocate the income.
Q4. If we use married filing jointly in MD, will my income be taxable (mine is not from MD source)
A4. Yes. You are a MD resident (My driver's license and vote are in Maryland). MD will give you a credit for the tax you pay NJ.
Q5. If we use married filing jointly for states, will both the states tax our income - will we end up paying more in taxes as we are paying to two states (double taxation?)?
A5. Effectively no. You just have complicated returns to do to allocate income and apply credits. You are at some risk of NJ calling you a resident for tax purposes and double taxing (only) your income. In that situation, one state will still (usually) give you a credit for the other state. When you file the NJ non-resident return, use your MD address, to ward off that possibility.
