Well running in the morning sounds like the only option for you. There's no optimum time to run, you just need to work out your daily schedule and figure out where you can fit running into it. If you're really tight for time you might have to split your workouts in two, but you lose some of the benefits that way, so only do that as a last resort.
As for losing weight, it's just a big numbers game: calories in versus calories out. Have a look at your diet and see if you're eating any empty calories (eg. potato chips, really fatty foods) and replace them with fresh fruit, vegetables or nuts. If you're already eating a healthy diet, then I don't think you should be trying to lose weight at all. As little wing hinted at, female runners have a very high risk of developing anorexia, so I think it's best not to tempt fate.