Translation:I teach English to my Japanese friends.
In English one can say "a car of pink color," but it is more normal to say "a car pink in color," and even more natural to say "a pink car" with no "of" at all. Some Japanese words for colors are not Japanese, so the word 色 is added to the foreign word. I don't think that it always needs to be translated.
As always, it all depends on context, so I concur with sneku-chan that it could be; nevertheless, I think the interpretation that is meant here is that of 日本人 (にほんじん, nihonjin) as “(all) Japanese people”, and thus 日本人の友だち would be “friends among the Japanese” — which is but a circumlocution for “Japanese friends”.
My comment needs double-checking, but this is how I understand this part of the sentence.
DL marked wrong my "I teach English to Japanese friends." Perhaps the students are friends to each other--I don't see "my" here anywhere. The reason DL marked my translation wrong was I used "I" instead of "we". Is this due to the beta testing phase being incomplete or can someone tell me what is truly wrong with the translation? Arigato. (and I don't agree with Gasezefe's comment here).
That is not necessarily "the reason" -- rather, it was marked wrong because it wasn't in the list of accepted answers, and the suggestion given was the "closest" one (by some metric). This will often show you what is wrong, but not always. (For example, if you've forgotten to write "a" or "the" in front of a singular noun, Duolingo often suggests the plural -- which doesn't need them, that is true, but the error is not the choice of the singular.)
I can't actually say if "my" is technically needed here or not, but if Duolingo accepts its absence with the subject "we", it should do so with the subject "I". You may want to report it. That said, I do think the version with "my" is more natural, and the reason there is no "my" in the Japanese is the same reason there is no "I" -- it is implied.
In terms of English grammar, one of the functions of the particle に is marking the indirect object. In this sentence, we have a direct object - the subject that is being taught to someone - and, an indirect object - whomever is being taught it. In this regard, Japanese is not far from English, as we use "to" to indicate indirect objects in careful, grammatically correct, speech, and that's one of the meanings of に.
"I teach English to my friend" vs "I teach my friend English".
There is neither "I" nor "we" in this sentence, it would be decided by context. Your problem was not that you chose the wrong pronoun, but something else (possibly missing "my", see above) that made your sentence not fit the list of accepted answers. There was, however, one with "we" there, and that one was considered to be the closest to your answer and was therefore displayed as the "correct" answer. The reason that that one was in the database, and not yours, is probably that it had been flagged by a user and accepted as correct by the development team, but they didn't take the time to look for variants of it to include as well (or at least they didn't think of your variant). So if it happens again, and you're sure that your sentence is otherwise correct, just report it. If it is, it will eventually be accepted.
Please remember, if you have not already, that Japanese tends to omit parts of a sentence when the context is known. So any subject that make sense should be accepted because English complete sentence needs a subject but it is impossible to know through the Japanese sentence alone.
I believe that "日本人の友だち" means that you are talking about some one who is Japanese (that is, "日本人"). To talk more generally about a friend in Japan, I think that would be expressed as "日本の友だち" (that is, a friend that somehow relates to "日本." Maybe they live there or you met them there, but they aren't necessarily Japanese).
How would the sentence sound if there was "I will teach" instead of just "I teach". Up until now duolingo didn't make any difference between present simple and future tense so I used them more or less interchangeably but this time it marked the future tense as incorrect. Can somebody explain this to me?