yes
Not very likely.
ask the DMV
VIN # check at the DMV
If the car's owner lost the title to the car a replacement title or duplicate title can be applied for thru the state dmv.
You should have gone to the DMV when you bought the car. They hand the license plates to you when you register it. If your state does it differently, you need to phone them or go to DMV.
You can apply for it at the DMV.
duplicate from DMV
No
You can do a DMV lookup by visiting the DMV website and looking for the options for DMV lookup. Searching for the title on your old car may not be possible if you are not the current owner.
she should go with your driver's license proving to them that she is eligible to do so. or at least somewhat of a note saying you allowed her to. i highly doubt the DMV will allow her to do that to a different persons car.
Many states do have laws which allow the DMV to deny registration of a vehicle by a person who is negligent in his or her child support obligations. The information will already be in the state's record system so there would be no need for them to contact CSE or CPS.
If it is paid off, see your local DMV.