My Latin is not great, so there may be occasional mistakes here, but here goes

(Note: I wrote this most of this post before modus irrealis's popped up, but I've tried to make sure my post agrees with it)
mredwin3 wrote:Quaedam officia sunt servanda etiam adversus eos a quibus iniuruam accepimus.
Certain duties are to be protected, even toward adverse things from which we taake justice.
I think you ended up trying to translate "adversus" twice: once as "toward" as in the footnote, and again as "adverse". Also, remember that iniūria means
injustice (think "injury", which is derived from this word, which is especially obvious if you spell it "injuria").
So I'm
guessing this is best read as, "Certain duties are to be preserved even towards those from whom we have received injustice."
mredwin3 wrote:Atque in re publica maxime conservanda sunt iura belli.
And even in the republic, the most important things are to be preserved by war. (Are servanda and conservanda future passive participles?)
I tend to think of "atque" as closer to just "and" rather than "and even"... it does seem to be more emphatic in some way than merely "et", but it's not really the same sort of emphasis as in the English phrase "and even".
It seems clear to me that this is a passive periphrastic, i.e., "we must preserve". I read "iūra bellī" as "the laws of war" (if I'm wrong anywhere, it's probably here). So I read this as, "And in the republic, we must preserve/maintain the laws of war."
mredwin3 wrote:Nam sunt duo genera decertandi: unum per disputationem, alterum per vim.
For there are two types to be fought: one with discussion, the other with force.
I think modus irrealis has this one: "For there are two types of fighting"
mredwin3 wrote:Illud est proprium hominis, hoc beluarum; sed bellum vi gerendum est si disputatione uti non licet.
It is propoer of man, this act of war; but war is to be carried out with force if discussion is not permitted.
Your translation of the first half of this sentence is rather odd. Don't forget to follow the footnotes. Don't forget the Latin idiom "illud ... hoc ...", which translates to "the former ... the latter ...". Hence, "The former [= discussion] is characteristic of man, the latter [= war] of wild beasts."
mredwin3 wrote:post autem victoriam ei conservandi sunt qui non crudeles, non duri in bello fuerunt ut maiores nostri Sabinos (what is this word??) in civitatem etiam acceperunt.
(I had a LOT of trouble with this one..) After, however, they are able to preserve victory, which is not cruel, they will not be harsh in war in order that out ancestors (Sabinos??) also took on citizenship.
"However, after victory, those who were not cruel, not harsh in war, are to be saved, just as our ancestors accepted the
Sabines into our state."
At first I thought "eī" was the dative of agent ("by it"), but I couldn't find the agent. I think modus irrealis has it: it's actually nominative.
mredwin3 wrote:At Carthaginem omnino sustulerunt; etiam Corinthum sustulerunt - quod non approbo;
But they destroyed Carthagin altogether; also they destroyed Corinth - which I do not approve.
That should be "Carthage" rather than "Carthagin", but yes.

mredwin3 wrote:sed credo eos how fecisse ne locu ipse ad bellum faciendum hortari posset.
but I trust them to not make this place that which might be urged towards creating war.
You've got some typos there: "how" should be "hoc", and "locu" should be "locus".
Crēdo can't be "trust" because crēdo takes the dative when it has that meaning. Here it's taking the accusative, so it means "believe". "But I believe they have done this so that the place itself would not be able to urge them to make war." (Again, modus irrealis's post helped me out here.)
mredwin3 wrote:Mea quidem sententia, pax quae nihil insidiarum habeat semper quaerenda est.
(Can't figure this out at all..) Indeed by my thought, peace may have no plot which it is always to be searching.
"Indeed, in my opinion, peace which has nothing of treachery must always be sought."
Let's put it all together and see what we have:
Certain duties are to be preserved even towards those from whom we have received injustice. And in the republic, we must preserve/maintain the laws of war. For there are two types of fighting: through discussion, or through force. The former is characteristic of man, the latter of wild beasts. Therefore, we must wage war so that we may live in peace without injustice; however, after victory, those who were not cruel, not harsh in war, are to be saved, just as our ancestors accepted the Sabines into our state. But they destroyed Carthage altogether; also they destroyed Corinth, which I do not approve. But I believe they have done this so that the place itself would not be able to urge them to make war. Indeed, in my opinion, peace which has nothing of treachery must always be sought.