tycker om is a particle verb meaning 'like'. In particle verbs, the particle, in this case om, is always stressed. The verb and particle work as a unit, but things like negations often tend to go between them. So it would be Jag tycker inte om en flicka if it were 'I don't like a girl'.
It might not be correct or literal, but using the phrase "I think on a girl" helps me remember that it means "I like a girl", if only because "tycker om" vaguely resembles "think on".
'om' is here a particle together with the verb to create the meaning 'like', and 'om' should have a stress in the pronounciation, which often is not present in the DuoLingo computer voice. 'Tycker' without particle means 'think', e.g. 'Vad tycker du?' (What do you think? as in having an opinion about something))
No, it is not a legitimate translation. 'Tycker om' in this sentence is about feelings you have, not 'thinking about'. You have to change the sentence, e.g. make it into a question, perhaps ask 'What do you think about this girl' = 'Vad tycker du om den flickan?', as a question about what your impressions is about a girl we have been speaking about earlier, presumably. And the answer might be 'I think she is rude' (Jag tycker att hon är ohövlig')
Thanks; that makes sense. I just wish we weren't presented translations with this level of nuance the first time a word is introduced. (I'd studied Swedish decades ago, but couldn't remember anything about "tycker om," so I looked it up when the sentence appeared. :/ )