It has been a while sense I was a jogger, so my knowledge is a little sketchy.
Don't jump out of bed and go into a run, its bad for your body, you need to get warmed up, get everything moving before you start. If I recall a delay of an hour from out of bed to first steps is a general rule.
Walking a mile and jogging a mile is the same thing (as indicated in previous post).
Have a cool down period after your run. Let your heart rate get back to normal before you consider yourself done (I use to use the last half to full mile for my cool down).
Running twice a day- not sure about anything related to that. I do have a suggestion however- try Yoga in the morning, and jog at night.
When I started Yoga the first time I found that twenty minutes of that really helped my stress and focus levels more so then an hour run.
Have fun, and give Yoga a try, its not complicated, or goofy, its really relaxing.