niego is obligatory after a preposition.
jego is obligatory at the start of a sentence and when contrasting two things.
go is used in most other situations.
When do pronouns precede the verb (ex. Ten kon NAS nie ZNA) and when do they proceed the verb (ex. My nie LUBIMY GO)?
I feel like it is more which part you want to be stressed. We usually have SVO word order, but also try not to leave pronouns at the end.
My go nie lubimy vs My nie lubimy go vs Nie lubimy go. are all correct and the difference is so small I might be imagining it.
Yeah, it would sound better, but we cannot change the default Polish sentence and it's not that tragic.
I should probably know this by now, but would 'Nie lubimy go' not work just as well? What is the function of 'my' if 'lubimy' is always 'we like'?
It would work just as well or even better. In some situation however we prefer to retain this unneeded pronouns, it is when we try to emphasise „we” or when we show some contradiction: „you do A but We do B”.
- Dzieci, pobawcie się z A. (Children, go and play with A)
- My go nie lubimy! (We don't like him)
I see, thank you.
In your example, would 'Go nie lubimy!' still be correct, just not preferred? Or would the meaning change slightly?
There is a rule that forbids us from starting a sentence with „go” and in fact it sound very much unnatural. Longer form: „Jego nie lubimy” is technically ok, but i wouldn't say it that way. For me the best is: „nie lubimy go”.
Leaving „my” has another rule here. Well, maybe it is better to translate the last sentence („My go nie lubimy!”) to: But we don't like him, „ale” (but) is not present here but slightly suggested.