no you cannot jump higher or run faster with them. If you want to jump higher, practice jumping. if you want to run faster, you have to practice running. do explosive exercises. Calf raise is an isolated exercise, so it only works one muscle. Running involves mostly the quadriceps and hips with the hamstrings. You have to train those if you want to become faster a long with the core (lower back and abs). Not just the calves or the calf raise exercise. Compound exercises/explosive exercises is what you need. Deadlift, squats, RDL, power clean, and so on (all uses multiple joint) are just example of compound/explosive exercises in the weightroom.
By the way - I am not a person trainer. I am just a poster, but I know this from experience and a class I took. Single Joint exercises are mostly for hypertrophy, and thats not what you want.
Also - the exercises you need depend on your goals and sport. What sport do you play, what strength and weaknesses do you have? You did not include this in your thread. Once you include it, the persona trainers may be able to help you out more.
One site to check out - Sign up for a free trial session with them if you like.