No, not unless her name is on the title.
There are a few variables here, but, yes, it is done all the time.
You can only trade in a car that has clear title. Depending on the dealership, it may work to bring the owner of the car with you to sign off on its being a trade. Or, get the title changed at the DMV into your name before shopping for a car. If this is your wife's car, think twice about doing it without her involvement.
The official title on both cars is present when trading to complete the trade.
You do not have to trade in your car where it was bought or purchased from. You may but you do not have to. However, you would probably need all the papers and reciepts to be able to do so.
Yes, you can do that.
car, wife, tv, pair of shoes
Yes. You must transfer the title.
If the car is titled in her name she will need to sign title to sell.
You need to pay off the present loan. Most people do that by adding the balance on to their new car loan, getting deeper and deeper into debt.
They will not take the no title car on trade.
no
To find the trade in value for a ford vehicle you need to find a website or car company which can tell you the value of your vehicle and decide who can give you the best price for your car.