Is the difference between vet and kjenner similar to saber and conocer in Spanish?
Yes it is! Where in vet=saber and kjenner=conocer
What is the difference between kjenner and forstår?
to know and to understand
What about "vite"?
Vite is to know something as a fact, kjenner is to know something as to be familiar with it. Compare to German Wissen / Kennen
Does "kjenner" just refer to knowing people, or can it be used to know a skill or a piece of information? (Like connaitre vs. savoir in French)
Yes. "Kjenner" can be used when you're referring to information that you're aware of, but maybe not something you know on a deeper level. "Jeg kjenner til det, men jeg er ingen ekspert." (I know about it, but I'm no expert.)
Could "recognize" also be an acceptable translate here?
"to recognize" is "å kjenne igjen". So the sentence would then be "Jeg kjenner deg igjen."
What is the difference between kjenner and vet?
"Å vite" is to know, as in a fact.
"Å kjenne" is to know of something or be familiar with it, such as a person, place, or thing.
If you've ever studied German, it has a similar construct. "Wissen" = "å vite" and "kennen" = "å kjenne."
Det er Wilson!
I danced with you once upon a dream!
Isn't kjenner sometimes used as to understand?
Jeg kjenner deg
Du kjenner meg
Én ting jeg kan si til deg er at du må være fri
Note for interest:-
"K_en" is also in English, used most up north and in Scotland.
Famous 19thC song, D'ye Ken John Peel?