If your are interested in improving your boxing/punching abilities, do that first, while your mind and body are alert, and work sharp. When you get tired, or doing a whole bunch of something, there is a tendency to just grind it out and get those reps done. That is counter-productive to learning to box.
As to your balance- and this will affect the power in your punches- there are a few exercises you can do, and they are posted on here- maybe under 'Useful Posts'? Keep in mind: when looking in the mirror, your feet should be under your shoulders, looking from the front or from the side. When you move forward, bring your rear foot with you. Getting the feet too far apart is a huge cause of loss of balance.
I'll bet you that the reason you don't have power in your punches is because you are throwing them- arm punching- instead of driving them. And the harder to try to punch hard, the harder it gets. Turn your hips into your punches- and this starts at the floor, goes through the hips to the shoulders, and only then do your arms move.
You'll need to spend a lot of time in front of a mirror, really watching what you are doing and correcting stuff immediately.