Does push up makes the arm big and if how many should i do?

Shoulders chest: Push up strengthen arms extensors ie triceps shoulder and chest muscles. An excellent exercise for development of those muscles. Will strengthen and some growth. As to number must be progressive increasing number over time. Should not perform same routine daily body needs time to grow and repair.

Yes & lots: Yes, push ups will increase the "caliber of your guns" and you should do as many as you can--realizing that sets are probably easier once get good at it--10 at a time, work to 15, 30, etc & repeat couple/few times daily.

Yes - lots: Going for big guns. These exercises help to build arm muscle: push downs, pin presses, dumbbell wrist curls, dips, rolling extensions, barbell wrist curls, preacher curls, chin ups, lying barbell triceps extensions, thick grip curls, concentration curls & lying dumbbell triceps extensions.