How do you eat if they have to cut out your tongue for cancer?

You adapt. As long as you have the back of your tongue and some of the front you can do pretty well with eating. The tongue helps to move the food around and back and the back of the tongue stimulates the swallowing reflex.
Yes most patients do. Most of the time, the tongue is only partially removed and the swallowing function is preserved. After surgery, it may take some time to get used to chew and swallow with only part of the tongue.
Depends. Depends on much tongue has to be removed and what type of reconstruction is performed. Acutely, patients can be fed using feeding tubes. As they recover and begin to take food by mouth, the tube is removed. In few patients, the tube feedings are permanent.