No. She must get a credit card in her own name since the guarantor on the account is deceased.
Use of a card that belongs to a deceased person sounds like fraud to me.
It is the deceased husband's name that needs to be removed from the deed. Contact the local court house to find out what you must do to claim the property in your name alone. Usually you can file a copy of the death certificate.
Take a copy of the death certificate to the local department of motor vehicles and they will get you on the right path to getting the title in your name.
Traditionally yes, however it is growing more and more common for a woman to add her husbands name, for both spouses to take the woman's maiden name or for both spouses to add their spouse name to their own. It should not be taken for granted that a wife's family name is the same as her husbands, especially among younger couples.
Only if the married couple resided in a community property state.