"Kateřina is not interested in them."
Translation:Kateřina se o ně nezajímá.
"Kateřina o ně nemá zájem" is certainly correct and natural.
"Kateřina nemá zájem o ně" strongly stresses "them" --- it works in contrast, e.g. "Kateřina nemá zájem o ně, ale o nás."
Also, I would say the meaning is slightly different:
"K. se o ně nezajímá." = she doesn't want/need to know about them, she is not curious, she is indifferent
"K. o ně nemá zájem." = she doesn't want them, she doesn't care about them
This is a subtle nuance and in many situations both phrasings can be used.
The pronoun forms that start with "n" are used after prepositions. You can find more information at this very handy site: https://en.wikipedia.org/wiki/Czech_declension#Personal_pronouns.
By now you know that these two translations have in common the placement of "se" after the first completed unit of meaning in the sentence. The other units of meaning can float around this second-place "se", more or less subtly tweaking the information structure in the statement, as if it were a response to a different question every time.
"O ně se nezajímá Kateřina" is technically not wrong, just very unlikely - you're doing some gymnastics with the word order (and thus intended meaning) here. Let me try to explain the difference:
"O ně se Kateřina nezajímá" stresses both "them" and the negated verb, because both of these units are moved away from their normal SVO position. Sort of like "Kateřina is not interested in them" - it's possible to imagine a situation where this would fit.
In your sentence you're stressing both "Kateřina" and "them" and it becomes excessively twisted - "Kateřina is not interested in them" - "It is KATEŘINA who is not interested, and it is THEM she is not interested in" - I can imagine this only in a dialogue such as this:
A) says something not quite comprehensible
B) What? Are you saying that they are not interested in Kateřina?
A) Ne! O ně se nezajímá Kateřina! (No, the other way around.)
But even here, the speaker could just say "Kateřina se nezajímá o ně" with the appropriate intonation/stress.
The verb is "zajímat se" (to be interested) and it needs the preposition "o" followed by the accusative case (in someone/something). The clitic "se" has to be in the 2nd grammatical position. That gives you: Kateřina (subject) + se (clitic part of the verb) + o ně ("in them") + nezajímá (main part of the verb).