"We do not like oranges."
Translation:हमें संतरे नहीं पसंद।
हमको is fine too. According to https://en.wiktionary.org/wiki/%E0%A4%B9%E0%A4%AE%E0%A4%95%E0%A5%8B हमें is a polite version.
The verb पसंद takes the person doing the liking as an indirect object (dative case) and the thing being liked as the subject. So हमें is the dative form of हम. Since the thing being liked is the subject, the verb is conjugated with respect to the thing being liked.
So for example, if the sentence was "we like the orange," it would be हमें संतरा पसंद है। Note that it's है not हैं because संतरा is singular and not plural.
I am not exactly sure how to answer this, and I hope that a native speaker can step in with more clarification. I do believe, however, that पसंद is an adjective, and not a verb, and usually नहीं comes immediately before the verb in a sentence, explaining the validity of "पसंद नहीं है". As far as the sentences where नहीं precedes पसंद, I believe this might have something to do with grammatical flexibility, or perhaps the optional omission of है/हैं in a negative sentence (a sentence using नहीं)... sorry I couldn't help more, as I am also learning!