So you believe it is harassment for say, a little old lady to gently say ‘I think you might have the wrong bathroom love!’ To a boy she sees looking at her in the womens changing room where she is half nude?

I don't believe that’s harassment. But if the man says he is in the right place and the woman keeps pressing him then yes that would be harassment. Here is a post from the old GC where poster harass a trans woman in the restroom.

https://archive.ph/IPJI4#selection-2051.0-2058.0

Was shamed last night for asking why there was a man in the women’s restroom.

I heard the voice of a man through the stall door at a bar last night and was taken aback. Why was there a man in the women’s restroom??? I asked why he was in there and was yelled at by him and his friend for misgendering him. We’re being shamed in our own restrooms now for legitimate questions of why a male voice would be heard in the women’s restroom. I’m so angry.

That is an example of harassment. One person even commented "The bar owner should step up against aggressive behaviour." even though no one was being aggressive per the OP.

A man is at the sink of the toilets taking photos of himself and a woman is asking him to please stop using a camera in a private space. Harassment or not?

Cis women also take photos of themselves in public restroom mirrors. I haven't seen it in person, but I have seen Facebook photos of what is obviously a public bathroom. If cis women can do it, other groups can also.

Is it harassment to tell someone to fuck off and kill themselves if you notice they took a second glance at you? If so men harass me in the womens room not the other way around.

Men tell you to fuck off and kill yourself? I’m sorry you experience this. I also glance at people when I'm out on the street and no one has done this to me. I wonder why. I wouldn't say it's harassment unless they are doing it in a way where you feel like you must leave the area.

Is it harassment to go deliberately linger around someone that you are aware is frightened of you?

Depends on the context.

Is it harassment to not correctly guess that a random man would prefer to be perceived as a female and to address him as a man?

Trans women are not men. I will use pronouns based on a person’s appearance. If someone tells me to use different pronouns, I will be happy to. I think it's rude to delicately not use someone’s pronouns.

Is it harassment to say “excuse me but I am uncomfortable” and to then leave?

No. You want to leave then leave. I also have the right to do this when I see you and it's not harassment.

Should women have any safeguards in public?

Everyone should have safeguards in public. It's not specific to women. I personally keep my belongings to myself so no one steals them or robs me. When I sell something online to a stranger we always meet in a public place, which has always been the local library because they have staff and security. I would never meet a stranger from the internet in a private place.

That said, if the "safeguards" you are referring to are "only X group of random strangers are allowed in this place but not Y group of random strangers" then no.

If you don’t care if I and other women want to avoid men, why do you make such a point to always mention how you don’t do that and always have some example of another woman doing it being bad?

If you want to avoid men, fine. If you want to run away when you see a man, fine. But you don't have the right to ask a man to leave a place that is open to the PUBLIC.

You cannot be unaware that I have never included transwomen when using the word women. If I am referring to transwomen I will say transwomen or men so as to be accurate and clear.

I guess I speak a different language than you but when I hear women I think all women, cis and trans. That's how I use the term myself. Sometimes I use the term women to refer to people who outwardly present as woman, regardless of their birth sex or how they identify when I'm talking about sexual harassment, etc.