Can one get rid of FUPA with proper diet and exercise?

Recommend that you set up a virtual or in-office consultation with a Board Certified Plastic Surgeon to obtain a specific rather than general response to your question.  Providing photos for the virtual consultation would likely allow the surgeon to determine if the pouch is due to fat deposits or skin laxity.  If fat deposits, liposuction would correct the problem; if laxity, a small incision below the bikini line may be required.  

It’s always advisable to try a healthy diet and exercise habits to try to reach your target weight and ideal body shape before trying liposuction or other body contouring tools. However, excess fat in the pubic area can be difficult to address entirely through diet and exercise alone, so you may want to consider liposuction once you’ve come as close to reaching your target weight with diet and exercise. Best of luck!

As you lose weight, the size of the area should get smaller.  As long as you don't have extra skin, this should be satisfactory.  If you have a lot of extra skin there, though, weight loss may not be enough.

Fat can reduce in volume with diet and exercise. If it is loose skin. then diet and exercise will not help.

Not likely. If you are young, a thorough liposuction of the pubic area commonly gives a very rewarding result. No need for wiz-bang additional treatments.In older patients, I combine liposuction with what I call a reverse mini tummy tuck to lift the pubic skin to a higher level.The same goes for both men and women. When this happens in men, the pubic skin hangs over the base of the penis.

Typically this is a very hard area for women to improve with diet and exercise.  Now you can combine more superficial liposuction with a BodyTite treatment to get both skin tightening and fat reduction.