If I diet exercise and lift weights will that help get rid of man boobs and give me firmer pecs?

Maybe! If your man boobs are simply adipose tissue, probably. However, if due to high estrogen levels in blood, usually not. Obesity causes high Estradiol in men. Also, taking excess testosterone can increase breast tissue, by being converted to Estradiol by cyclic aromatase.
Moobs. Definitely. Focus on chest exercises to make sure you have decent pecs underneath the fat you are planning to lose.
Yes. Yes, exercising and dieting will help reduce the total amount of fat in your body. You should also refrain from smoking.
Yes. Balanced diet and regular exercise will definitely help - stick with it though - it may take a few months.