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That one's also part of German. They have umlauts for A, O, and U. Though as far as I can tell, the German Ä is just a variant of "E".

The other two are their own vowels, and they used to be rendered in English as "oe" and "ue". It's not clear to me why we decided that it was better to write "Gödel" as "Godel" than as "Goedel".

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Why used to be? I still see on a daily basis and I think I never saw ö rendered as o (when the writer knew what they were doing)

He probably wanted to get Email, when Umlauts weren't in the spec yet. I don't know though, I totally made that up.

It's not difficult for English speakers to write "e".

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