Q1: Why don't hermaphrodites show that in other sexually reproducing species sex is not a binary?

Not a binary as opposed to what?

You can cut a worm in half and both halves will live... so why can't we do that with humans?

Hermaphrodites only show that sex is still binary—but that in some species both sex organs exist together. These animals inseminate each other, similar to plant pollination. It still takes two.

You won't find a hermaphrodite species that has male individuals separate from female individuals, just as you won't find a human that is both male and female in the same body.

Q2: Why is sex not a bimodal distribution?

This sounds like wordplay on what "binary" or "bimodal" means and conveniently mixing up what you want to apply these terms to.

Digital computers are binary. Digital logic is the purest mathematical example of a "binary" you can find. You can work out the theory in black & white on a chalkboard, and irrefutably show that there are exactly two states to work with. Your computer has millions of transistors in it that all work in concert using binary logic—which proves the theory in practice, beyond any doubt.

You can plot a digital signal on an oscilloscope. In a perfect theoretical world, it would show a square wave with 90° corners where the voltage switches from 0 to 1. But that's not what we see: if you look at the edge of the transitions, it ramps up and ramps down because of the quality of the physical device it's built on. It has some overshoot and waviness. It's noisy.

When you build a computer that works on physical things like the voltage levels of electrical signals, or reversing the polarity of magnetism, or the presence/absence of an optical signal, you can run into more severe imperfections. Does a bad sector on your hard disk which can't be reliably read as a "1" or a "0" because of weak magnetization imply that the theory of binary logic needs to be revised? Does it mean the concept of discrete "1" and "0" is actually a bimodal spectrum? Of course not.

(Yes I'm aware of quantum computers and qubits which operate on statistical probabilities between 1 and 0. But that's a different theory outside of digital logic: it has no binary axioms.)

Q3: how come they are not less of their sex for losing those abilities and are not of a different sex category after the removal of all genitalia?

I leave you with this:

Plato was applauded for his definition of man as a featherless biped, so Diogenes the Cynic plucked the feathers from a cock, brought it to Plato’s school, and said, “Here is Plato’s man.”

I'm not sure why you're so overly concerned with any of this. It's a bit obsessive to dwell on the rarest exceptions and abnormalities when everything else in your personal experience shows that sex is binary. Ask yourself how many people you've ever met or heard of that you honestly couldn't tell me were born as exactly one or the other sex, such that even their doctor couldn't tell. Then ask yourself who are these people arguing about whether sex is bimodal: you know for a fact their own sex is also just one or the other. They are looking to justify their social issues by trying to find a "gotcha" in biological exceptions that they don't even qualify as.