Community property is property acquired during marriage. Community property also includes income and debt during marriage. Each spouse has a one half interest in the community property.
Separate property is property acquired before marriage or after the marriage ends. Separate property also includes income and debt before marriage or after the marriage ends. A spouse has no claim to the other spouse's separate property. Separate property also includes property, income and debt after separation with no intent to reunite.
If your wife is able to work, she won't be eligible for SSI.
The debt that was incurred during marriage is community property. Both you and she remain liable for that debt.
Since your car was purchased before marriage, it is your separate property; however, if your auto loan payments during marriage were made from income during marriage, those payments are community property and your wife would have a claim of half the amount of those payments. If your auto loan payments during marriage were made from income prior to marriage, those payments are your separate property and your wife has no claim. If your auto loan payments during marriage were comingled and cannot be identified as paid from income before marriage (separate property) or income during marriage (community property), there is a rebuttable presumption that the comingled payments are community property to which your wife would have a one half interest.
You could buy out her community property claim on the loan payments and you can keep your car. If the loan payments are community property, it is possible for there to be an agreement to an unequal division of community property in which she would receive less than half of the loan payments that are community property.