As far as your rate, I always bill as high as I can without pushback. Where is that level? You'll know when your rate is too high. I kept increasing my rate with contracts until clients started to grumble a bit. Then I backed it off 10% and haven't had a problem since. Note this means I am getting paid 30% more than where I originally started. Wouldn't have known that if I didn't attempt to max out my rate.
In the end it's just business. You either make a client happy or you don't. As a business your goal is to maximize your profits without much pushback. That will just take some time and energy to find out what the market will bear.