Hi! I wouldn't anticipate losing muscle by engaging in cardio; instead, the fat layer you melt away will only augment your musculature. It seems you'll simply end up looking leaner and "tighter" than previously. Why don't you want to continue with the lifting, though, in conjunction with your running? This is what I do and it's the best of both worlds, as the increased muscle mass aids your body in burning a greater amount of calories at rest. If it's an issue of time where you must choose running or weights, maybe switch off every other day.
Re: gaining speed, I've found that if you want to run fast, you must...run fast. Similarly, to increase mileage you must run farther. I don't mean to oversimplify here but to use an extreme example, one can't learn to pace herself for a marathon by running sprints, nor can she learn to increase her short-track speed by jogging cross-country distances. I just run, say, 7 minutes at a certain speed, then rest for one minute, then 7 minutes at a faster speed, then rest, etc. for the duration of my run. Maybe bump up your speeds once per week or two. Happy running!