Will it damage my phone if I download long and short-term episodes on Netflix?
No unless you download it with a hotspot then it damages your internet
How should that hurt?!
No, except that the devices are not made for such a constant load. The battery goes to its knees relatively quickly if you use the device all day.
The internal memory
I do not know. I'm not a technician. But on the PC e.g. Constant downloads and deletions damage the PC.
No. "Harm" is wrong. Every memory "wears out" at some point, but that is negligible with a smartphone.
It's a more theoretical problem. A modern smartphone will not show any noticeable "wear and tear" on the internal memory if you regularly save films.