Dear Ashutosh,
Here are the answers to your questions.
1. Can I get directly temporary residence visa for Lithania from here in India in Lithuanian Embassy ?
It is possible to apply for TRP in LIthuanian embassy in India, but you need to have solid grounds to apply. For example having a company in Lithuania, or having employment there or some other solid reason.
2. If yes, then what will be the documentary process step by step & what will be the total expenses (embassy fees) ?
Well, your application will be reviewed for 6 months, and if all goes well, you may get the TRP card after 6 months from applying. Documents depend upon your reason of residence permit. Cost will be about 100 Eu per person for application.
3. What is the school admission period (month) of Lithuania, and in which month schools open.
September, that's the month when all academic activities begin here.
Good Luck!