> I also want to activate the minor-mode globally.
> How could I activate a minor-mode globally?

I also want a falafel.  Or a burrito.  And a beer.  Right now!
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Have you tried to *ask Emacs*?

Start with `C-h f define-minor-mode'.

Check the Emacs manual, with `i minor mode'.

Check the Elisp manual, with `i minor mode':

https://www.gnu.org/software/emacs/manual/html_node/elisp/Defining-Minor-Modes.html
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You'll generally get more, and better, help from Emacs itself.

And having _tried_ to *ask Emacs* you'll generally get more, and better, help from mailing lists and online Q&A.

(Just a suggestion - unsolicited, free advice.)

And no, it's not obvious at the outset how to ask Emacs.  But that's really the first, and the most empowering, thing to learn.

Ask Emacs how to ask Emacs...
Ask Elisp how to ask Elisp...