If you and your wife are filing the I-751 Petition to Remove Conditions on Residency together, you will be required to provide documentary proof that you are in a good faith, bonafide marriage. It does not mean that you have to add your wife's names to your business or house but if you have other evidence of living together, combined finances, assets etc. it should be ok. You should consult an immigration attorney to discuss this further.
Disclaimer: The information provided here is generalized and should not be relied upon as legal advice. This communication does not create an attorney-client relationship.
Not necessarily if you have sufficient other proof of a life together and the bona fides of your relationship, but it could help depending on timing (i.e. it's probably not a good idea if it appears like you are only doing this for this purpose). I also strongly suggest you work with an attorney who practices primarily or exclusively in immigration law, so you can get the assistance of someone who deals with these matters regularly and is experienced in how to advise you best. Good luck.
Gunda J. Brost Brost Law Office This advice does not form an attorney-client relationship and is merely informative. It should not by itself be relied upon to address a legal concern.
No, you don't have to add your spouse's name to the title of the house, cars etc. You will need to prove that the marriage was entered in good faith. There are several ways to do this. Start by reading the instructions to Form I-751. If you need help, consult an immigration attorney.