For your goals, you need to lose fat and that means only two things...
- More cardio exercise
- Less calorie consumption
The pushups are ok if you feel you need some upper body strength but in as so far as your stated goals are concerned, they do absolutely nothing towards losing fat.
You say that you cannot control your diet. I cannot see how that is possible. Everyone can control their diet. If you cannot change the actual food you are eating because someone else is cooking it, then you can at least reduce the portions of the food you eat and that will reduce your calorie consumption.
Incorporate some cardio into your workout. Start with a nice 30 minute walk at least three times a week. After a couple of weeks, speed up the pace and keep doing that until you feel comfortable running for 30 minutes three times a week. By that time, you will be lean and healthy and you can move on to heavier training if you want to.