MONITOR YOUR STRIDES
When you run on a treadmill, your stride isn't as natural as when you run outdoors. This is because the treadmill dictates your stride: the cushioning is even, the pace is constant, and your foot's contact with the ground is slightly different. This leads to you taking smaller strides than you would when running outdoors.
Another thing to bear in mind is that when you use a treadmill you feel as if you are running faster than you actually are.
To run at the right speed with the right posture, take ten minutes before your session to warm up (set the treadmill at 2-3km/h, for example) and then spend a minimum of 20 minutes running, increasing the intensity and the incline as you go.
If you want to have the same level of intensity as an outdoor workout, try to take the same size strides and listen to your body to dictate your pace.
In terms of breathing, don't forget to breathe in and out properly. It's important to breathe comfortably throughout your workout. In other words, you shouldn't feel completely out of breath.