Suppose a boy made an MMS video of a girl taking bath and then asked her of sexual favours with a threat to circulate the video otherwise
This is Voyeruism IPC 254c, and Sexual Harrasment IPC 354A.
Next the girl didn't budge so he called her mother in front of her threatening with all the above.
This is also sexual harassment.
Suppose the girl, in a fit of rage hit that boy, not with the intention of murder, and the boy died.
No guilt here, if the fit of rage happened while he was threatening - that's self-defense and without punishment. In fact, you can't even charge assault, because Assault under IPC 352 explicitly says it does not apply to grave provocation. So the more specialized IPC 358 applies:
Whoever assaults or uses criminal force to any person on grave and sudden provocation given by that person, shall be punished with simple imprisonment for a term which may extend to one month, or with fine which may extend to two hundred rupees, or with both.ExplanationsThe last section is subject to the same explanation as section 352.
I don't see that IPC 304a could apply in its negligent part, as no duty of care exists. I don't quite see how a provoked act might qualify as a rash act, but it might. It's clearly not murder under IPC 300, as there's no intent. Also, IPC 299 does not apply either: that too requires Intent.
So the worst available is at maximum 2 years + Fine, but it's much more likely that we are dealing with assault after grave and sudden provocation, so about one month or 200 rupees.
Oh, and now comes the kicker: You said girl. That implies below 18. As a result, the Indian Juvenile Justice Act 2015 applies. So the two possible sentences... Both are classed as:
Chapter 1, 2. (45) “petty offences” includes the offences for which the maximum punishment
under the Indian Penal Code or any other law for the time being in force is imprisonment
up to three years;
As a result, the trial will be in front of a Board described in section 14 and has to be done as a speedy summary proceeding.