I've never been able to lose weight without exercise, but many people do.
Cutting simple carbs, such as those found in sugar, products made with white flour, white rice, most processed foods will go a long way toward helping you lose weight.
Center your meals around veggies, high quality/low fat protein, such as lean meats, low/no fat dairy, eggs, nuts, seeds, whole grains etc.
Most important is to make water your beverage of choice. Even diet sodas will not help you lose weight.
Yes. Exercise doesn't generally help people lose weight unless you start running - but exercise DOES help you stay motivated to stick with your diet and turn down the donuts, etc.
Any diet will work if you can stick with it. Many people find that a low-carb diet helps to reduce hunger (Atkins Diet). The "South Beach Diet" is a little more flexible but also seems to be very effective. For some people the defined meal plan type diet, such as Jenny Craig, works well - you buy their food and don't eat anything else, and that way you don't eat too many calories. I have had more patients lose weight and keep it off with Weight Watchers than anything else - Weight Watchers will teach you how to lose, and if you go to meetings you have to be accountable for your weight loss (or not) - and that helps with the motivation.
Yes, although progress is likely to be slower than by including exercise. Even when you feel like you are doing little or nothing, your body is 'exercising' itself, and you will still be burning calories/fat. Including a daily amount of even light exercise - 30 minutes of moderate walking, for example - will have much better effects, however.