Will running on flat ground slim my calves down and tone them up as i really want slim but toned calves??

Well first thing to note is that muscles only really get larger by increasing the amount of weight they need to move. On the other hand repeated exercise with a more or less static weight (your body) will help tone and endurance. So running will never make your calves very large but it will tone them up. As far as slimming, yes running on flat ground will slim down your entire body. This is assuming you diet as well and have fat to lose. There are other exercises for your calves, you can stand flat on your feet and then pop up on your toes and then repeat. You can change the way your feet are pointed to work different parts of the calf. You can also do this with your toes on the edge of the stairs facing upwards. As TOWEL mentioned stretching is vital. Do yoga. Also of note is that you can make very fast progress stretching if you spend the time doing it. I went from not being able to touch my toes to being able to touch my knee to my forehead with a locked knee in less than a month.

Sounds like you have big calves by nature. Riding a bike will help to tone them as will running. Don't focus on one area of your body that you don't like and try and change it. Focus on your whole body and develop it. Learn to like your calves and make them stronger and bigger. Use them to your advantage.

I noticed that running on a treadmill works the calves a lot more and the hips and thighs less. Treadmill running is cheap running as their is no air resistance on the torso, but I do it with slight 2% incline (or more) and the calves really feel it more, especially when you are not accustomed to it. Calf raises on various machines also bring some tone and strength.

Exercise cannot target what fat to reduce. Fat will come off first where it went on last. If you want fat gone, you need to do the most-fat burning exercises you can, and not try to target anything. To burn off fat you want to use the biggest muscles and the ones that recover the fastest. That'll be your core and upper legs. Running is good for the legs if you run fast and hard. Deadlifts are an amazing fat burner but women typically avoid them because they have some irrational fear they'll get big bulging muscles from it or because it doesn't feel girly enough.