Learn Spanish (Latin America): Quiero editar tanto el episodio uno como el dos.

While tanto usually means "so much" and como means "like" or "as," when you pair them up as tanto [A] como [B], they form a fixed expression meaning "both [A] and [B]". In this sentence, it emphasizes that you want to edit the first episode just as much as the second one.

If I were talking about a feminine noun, like la temporada (the season), would tanto change to tanta?

No. When used together as a conjunction pair (tanto... como...), tanto does not change to match the gender or number of the nouns. You would still say: Quiero editar tanto la temporada uno como la dos.

Why is there an el before dos? Can I just say "como dos" like in English?

In Spanish, when you connect two specific nouns with tanto... como..., you usually need to keep the article for both items. Saying el dos is short for el episodio dos. If you dropped the el, the sentence would sound incomplete to a native speaker.

Why does the sentence use episodio uno instead of primer episodio?