Well, if you're talking about the Latin tribe, I suppose the first one would be Terra Latinorum, though Google Translate suggests that Latine loqui populo terrae is sufficient for "land of the people who speak Latin".
Their republic would then be either De re publica Latinorum or Latine loquentium re publica populi terrae and their port would be portum Latinorum or portum qui Latine loqui.
Terra Latinorum,
Fines Latinorum,
Regio Latinorum (probably the best)would all be valid. You've muddled the grammar in the longer ones -
Res publica Latinorum is 'the Latins' way of doing politics' (see below), and there's a problem in that last because
loqor cannot be passive (it's a deponent verb, meaning that its active form looks passive anyway):
Portum ubi Latine loquntur 'the port where they speak Latin' is probably the best.
It's republica, not re publica
Both are valid; written Latin didn't actually use spaces until well into the Middle Ages - a consequence of having a mostly-illiterate population is that the writing system doesn't have the same pressure to evolve to be easily legible: it was considered 'odd' that Julius Caesar, a man of huge intellect, was able to read silently. Res Publica means 'a public [as in 'public sector'] affair' and meant 'politics', and then 'our way of doing public matters' as distinct from that of foreigners - and therefore 'republic'. I don't
think that a foreign republic (although I imagine 'res publica sua' to mean 'their political system' would have been valid) as we understand the term - as in 'Republic of France' - would have been referred to in the same way;
The Republic was an intrinsic part of the phrase - but I could be wrong.
I can imagine
Polis might have been borrowed from Greek to describe a city-state run as a republic, if that helps.
My father always bemoaned that I didn't do grammar in English, let alone in any other language, and my Latin knowledge is entirely armchair variety. I will cede the floor willingly.
Ah, I'm of the generation that did A-Level Latin back in the day because that's what
educated people did!