Welcome to the site, Far3. It's not likely that you're burning muscle for fuel if you're running for less than an hour. The body has glycogen stores sufficient to last a good couple of hours. The body's preferred energy sources, from what I understand, are glucose/glycogen, fat, and then muscle. We need protein during recovery mainly to provide the body with sufficient material to repair muscle damage. (It's a good idea to get something into your body after an intense workout -- the optimal ratio appears to be 4:1 carbohydrate to protein, with one gram of carbohydrate per pound of body weight. Half should be consumed within 30 minutes, the remainder within the following 1.5 hours. This is from an article on the McMillan Running web site.)
As far as whether or what to eat before your run, well, that's a more a matter of personal preference. For shorter runs (say, less than about six miles), I typically head out the door on an empty stomach (maybe some water or tea). For the longer runs, I like to eat a Clif Bar about a half-hour before heading out. Some people eat a half-bagel with peanut butter, some folks a banana, maybe oatmeal, and still others just have some coffee. You'll need to try out different things to see what works best for you.
Don
"Don't fear moving slowly forward ... fear standing still" - Kathleen Harris
"Last is just the slowest winner." - C. Hunter Boyd