"My parents do not like that you eat ants."
Translation:Mina föräldrar tycker inte om att du äter myror.
I'm starting to notice a pattern with words ending in "er". That pattern is that these words, when in plural form, now end in "rar". For example, "my sister" is "min syster" and "my sisters" is "mina systrar".
So, maybe that can help someone who is having trouble with this type of plural formation.
No, om is not a preposition here, it's a particle and always stressed. Since the verb is in second place in main clauses (that are not questions), inte goes after the verb there unless it's at the start of the sentence, which is very rare. In subclauses, inte goes before the verb. There's a longer post about word order here: https://www.duolingo.com/comment/8970470, but with relation to phrasal verbs, inte goes between the verb and its particle. So either inte comes before all of tycker om, or it will go between the two words.
You're thinking correctly, it's just that att is a conjunction here, so the second clause functions independently. Hence, it follows normal word order for that clause, just as if it had been its own sentence - which means the v2 rule applies to it as well.
(This is not actually strictly true, because adverbials such as inte will still be placed in front of the verb. But it usually helps to think of it that way.)