How can I manage my time and day plan to prepare for IITs?

Don't worry much about time, just concentrate on what you are studying in school and coaching. Apart from that just revise what are you studying daily and do practice as much you can whenever you get the time and don't forgot to take a good sleep of 7-8 hours.

You are aiming for IIT, then you must have to do hard work. Focus on your goal, concentrate on what you learn on daily basis. Practice as much as you can, revise content on regular intervals. Because a year hard work can let you to a bright future. Hopefully, you achieve it. Best of luck.