How do I increase punching power?
Lift for power. Use mid range reps per set (6-8) with whatever weight you generally use for those reps and lift as fast as possible then lower the weight in control. You really need to workout your whole body but probably focus on chest, shoulders, and triceps (bench press). Also eat plenty to add lean muscle mass but remember there is a difference between lifting for power and lifting for size.
Do push ups and pull ups increase punch speed and power?
All these things can but I think you are looking at things in too simplistic of a way really. Reducing ones weight if they are overweight will generally make them faster but what about a person who is not overweight? Doing things like push-ups and pull-ups can help increase your reflexes and speed but so can some other exercises or approaches to them as well or even better actually. One of the best ways to increase speed and power that I have found is doing plyometrics and also circuit type weight training. Many of your college and pro athletes today's use these approaches for enhancing their own speed and power and there are even sports training places built up around major metropolitan areas that a person can go and enroll for this purpose. Many of them offer programs starting at the grade school age level even and go up from there. I would suggest you look at some plyometric training programs and have attached a website to help get you started. Also if you look at some plyometric workouts they will include clapping push-ups for increasing punching speed and power. While that is not exactly the same thing as a normal push-up it is a push-up and also is a good example of what I mean when I say you are looking at things somewhat too simplistically. Even if you don't combine plyometric workouts with circuit type weight training it can have a huge impact on your speed and power so check out the web site and consider adding a plyo type workout to your routine and doing that 3-4 times per week. A plyo workout only takes 15-30 minutes depending on how extensive it is so add one to your routine for a few weeks and I bet you see results in less than a month. http://www.sport-fitness-advisor.com/ply...
What can improve punching power?
Also the heavy bag swinging is not really an indication of power... if the heavy bag 'flies' then it is most likely an indication of poor technique. You want to hit the bag, not push it. Watch this video of Mike Tyson hitting the bag... he is making it swing before throwing punches on purpose, but notice when he hits the bag it is not 'flying'. http://www.youtube.com/watch?v=dDy41yxwb... I tried to find a good video to demonstrate what i am saying about hitting not pushing, but i failed to find a good one. You want to make impact with the bag near the full extension of your arm, and penetrate a couple inches into the bag... the goal is not to punch through the bag, but into it. You'll get a nice satisfying crack sound if you are hitting it properly.