That's how couples in Norway usually meet.
"Through sacrificing her bike!"
Is å redde (to rescue) related to redd (afraid)? If you're afraid of something, you need rescuing from it?
Not a bad guess, but no.
"å redde" has German roots, while the adjective "redd" comes from the Old Norse word for "to scare", "hræða", (think "to make afraid").
Is "redder" also used in the context of saving a file or saving money, or is that a different word?
I think the verb for saving money is å spare, and for saving a file it's å lagre. The meaning of those being something like "to put aside" and "to store", respectively. A native speaker can perhaps confirm.
That's correct. You can use "å lagre" with other things than files, but then it would indeed translate to "to store" rather than "to save".
why is lagrer not correct?
You would use that when saving digital files, but not people.