Doubt you'll get paternity leave unless you voluntarily back term yourself and I doubt they'd led you be away from the Academy for a long period i.e. you'd need to be in Lucknow with the evening/weekend allowed out. I'm sure if you wrote a letter to your Coy Comd you'd get the day off but that's probably about it at RMAS unless you want to start again. I had a friend who left at the end of juniors for comp reasons and had to start again when they came back.
The rules on OPL are 26 weeks in current job...don't think TA counts as employment so you'd have to count from day 1 at RMAS...if you meet the 26 weeks in then you are probably entitled....don't think the Army have an exemption