FHA Home Inspections, Inc.
And you need him or her before you put in any money. These are complicated legal issues and with so much money at stake, don't be foolish. Get yourself a good real estate attorney now. Ask for referrals from friends who have bought/sold real estate.
It's always best to consult with an attorney on these matters, but as far as I know, NJ has "no fault" divorce, which would probably result in the splitting of assets. The deed is a separate document from the mortgage and needs both signatures to be changed. As far as logistics, it's good to create a clear paper trail.
It really does not matter if you are or not. Since you are married and this is the marital residence you automatically become 50% owner of the property. Now if the mortgage person suggests that you stay off then you should stay off.
If you do stay off the deed/title and use the proceed from your other home you can still use it as a downpayment.
For all your other questions I would recommend consulting a attorney about protecting your assets. Feel free and call Laura Kozma, Esq.. She is a real estate attorney that I use all the time and she will be happy to answer any of your questions without charging you a fee. Her number is 609-208-1301.
Hope this helps,
Oh, and by the way, if you need an agent feel free to drop me a line.