The Mishna states
I'm curious how you know this particular clause from the Mishnah and not know that what you state is actually subject to a Tannaic dispute.
Is this an absolute majority?
See Horayos 1:5. As a quick summary of the various opinions recorded there:
R' Meir: 50% of the congregation (even of six Shevatim) or 50% of at least seven Shevatim ...
I really can't see how you got this from the Gemara.
Read the words on the "intimidating" speech carefully, it's not intimidation.
We just tell her the sometimes people do mistakes, even great people, so she will feel more comfortable to admit if guilty (among other actions we do, see Mishna 1:6, 3:3. ).
We don't describe the horrible effect of the water on ...