The biggest mistake all beginners make is running too fast
If your stomach starts to hurt, simply slow down and the pain should become less. Do note that you shouldn't start running straight after a meal, as this can also cause pain in your stomach. But most of the time you're simply running too fast. Instead start running at a speed that you're still able to hold up a conversation. You'll be surprised how slow this may seem, but your pace will start to increase soon enough, so just be patient.
Furthermore, while its not entirely clear how you alternate jogging and walking, I recommend you start following a proven training schedule, such as Couch 2 5K. This makes sure that you don't run for long stretches at a time, while you're not ready for it yet. Instead, it gradually built up the duration of the running intervals and the workout in total.
As for the pain in your calves, this too is a result of you running too fast and too long. If you start to follow the C25K plan, you shouldn't have any problems with but your stomach and your legs. If you do: again, you're running too fast, so slow down!
Good luck and be sure to come back if you get any other questions as you progress!