Bench press is not the same as push-ups. BP is normally used for the chest when heavy lifting, while PU is normally used to strengthen the chest, back, and abs. The problem with PU is that the weight you use is not very heavy, so it is high reps with light weight. It is still great for you, but doesn't have the same bulking effect as BP.
Yes. Eat only when hungry and not more than thrice a day. Nothing other than water in between. Include plenty of uncooked vegetables and fruits in each meal, preferably 50%. Chew each morsel at least 32 times to activate ur body to generate signals of hunger/fullness. Obey these signals. Take light exercises and brisk walks regularly preferably twice a day. U will achieve what u have not even dreamt and that too in a reasonable time. Do not be in a hurry. It is however to be noted that one cannot change the shape or size of different parts of the body.
with bench presses you have more control over the weight you lift
No. Pushups are totally different. Try doing ten pushups then ten benches. DIfferent parts of your body hurt right? So quite simply, they aren't the same.
Bench Press is not the same as doing pushups because it is more concentrated on the chest. Pushups work the chest, arms and abs. The area of the chest that is worked is also different. A great strategy is to do Bench press and top it off with some pushups. Good Luck!!