How far a finger need to go in to break a hymen? does a finger need to be deep in to break the hymen?

It's not distance: First, in the normal life of girls and women, the hymen is and shall remain irrelevant so that her society is unable to use hymens as a means of bias or discrimination towards girls or women. Secondly, when deciding how to (or how not to) make an opening wider, the distance a finger or penis is inserted is not the issue. It's the diameter (or type of motion) of said finger or penis that matters.