Is it possible to gain muscle and reduce fat at the same time?

Yes. You can lose fat and gain muscle, by consuming a high protein diet, and reducing your calorie intake. Read the section about tracking your calorie intake. Do interval training twice a week getting the heart rate up to 85% of your maximum each time and do 300 minutes of moderate intensity cardiovascular exercise, preferably in 30 minute continuous sessions or longer. If you perform strengthening exercises like lunges, jumps and squats you will build muscle. Good luck. It takes will power to change you diet and exercise habits, but it can be done. Be strong and believe in yourself.