2003 Ford Taurus What do you suggest for transmission/engin

I had a sensor go out on my Taurus and the Ford house wanted to do a "push" or a flush for my transmission for maintenance. My dad was a mechanic, seems like I remember him saying "don't
flush transmissions". I called a trans shop and they said they don't recommend it. What is your opinion?

Additionally, if my timing belt breaks, will it hurt my engine like my previous car (Honda) or will it just stop?

Any suggestion how to tug a couple of more miles out my fuel consumption-this car is a gas hog.