Why does .woff2 show up with two different MIME types?
Because web fonts were originally registered under the application/ top-level type, producing application/font-woff2, and only in 2017 did RFC 8081 create the dedicated font/ type, producing font/woff2. Older servers still declare the legacy form, so both stay in use and both get decoded by browsers.
Can I trust the extension to know the real type of a user-uploaded file?
No. The extension is chosen by whoever saves the file and can be changed freely without altering a single byte of the content; a .jpg file could contain anything. Servers accepting uploads should inspect the first bytes of the file (magic numbers) and never trust the name alone to decide how to process it.
Do .jpg and .jpeg have different MIME types from each other?
No, both (and the rarer .jpe variant) resolve to the same registered type, image/jpeg. The three-versus-four-letter difference is just a historical leftover from the old FAT/DOS three-character extension limit, which never existed in the image format's own specification.