My advice to students seeking advice is to partner-up with another student... I assume there is an electrical engineering department at your school? Maybe there's a robotics club?
*i have attached a screen shot of my circuit design from Proteus
It didn't get attached.
1.is my transistor choice good?
They should be able to handle the current (if heatsinked). A MOSFET would probably run cooler, but you might still need heatsinks.
Or, you can buy pre-assembled motor driver boards. (There is a popular H-bridge driver chip, but I've never used it and I don't know it's voltage & current ratings.)
2.is my electrical circuit design in Proteus correct ? Especially the H-BRIDGE circuits?
If I could see your schematic I might notice if something's wrong, but personally I wouldn't be comfortable "approving" your design.
3.how much resistance should i use to protect my arduino uno board and to run the circuit SAFE ?
You don't put a resistor in series with the power. If you are running I/O lines to the "outside world" you can sometimes use resistors, sometimes along with diodes to protect the Arduino. But, in most designs there's no need for that... Design your circuit correctly and you won't fry your Arduino. (There is something called the [u]Ruggedunio[/u] if you want to look into what they do.)
4.should i use a capacitor in parallel with the motor, if yes what should be the capacitance?
No. If you get noise that causes the Arduino to glitch, you may need a capacitor or other filtering for the Arduino's power.
5.the motors that im using can go up to approximately 1875 rpm,but i want to decrease that to 10-20 rpm so how can i achieve that?
You'll have to do that mechanically (gears or pulleys). You can slow a motor with PWM, but without speed-measuring feedback it's impossible to get the "right" speed. Even with feedback that's very-slow, and probably impossible, especially with a load. And as you know, if you gear-down you'll get more torque.
6.what kind of diode should i use to prevent from back EMF?
The diode has to handle the same current as the motor. Give yourself some safety margin and get a diode with at least twice the motor-current rating. The voltage rating isn't critical because any diode can handle 24V or more (that's the reverse voltage rating).