During the selenelion, the sun and an eclipsed moon can both be seen at the same time. This is impossible on a round earth, as shown above.
You mean like this?...

Further, the typical diagrams of the earth's umbra and penumbra are not reconcilable with the RE constant assertion that the sun's light arrives in parallel rays because the sun is so distant. This undermines the premise of Eratosthene's famous "proof" that the earth is in fact round.
You're kinda right... The assumption that the Sun's rays arrive parallel is an
approximation. In reality, of course, they don't arrive parallel. But it's a very good assumption for small areas on the Earth's surface (like a city, or small country even).
But when you consider systems like the whole Earth or the Earth-Sun-Moon system, you can't assume they're parallel, which is why you get umbra/penumbra pictures like this:

Another note on how the
almost parallel approximation effects Eratosthenes' famous proof:
Eratosthenes assumed that the Sun's rays arrive approximately parallel, but of course they don't. However, this doesn't mean that the entire proof is incorrect. It only means that he was off by a small amount, proportional to the magnitude of the error. And since the error in the assumption is very small (because the Sun is very far away), the error in the result is small.
This is easy to see if you draw it out yourself, which I suggest you do before claiming this is nonsense. I'll put one up if you really don't feel like drawing it, but the best editor I have is MS Paint, so that'll be a pain...
Thanks