Duo now has a girlfriend called Duet. Thanks for the headcanon mate!

〜ませんか is used to extend an invite.

Read more here: http://www.punipunijapan.com/japanese-invitation/

Literally translated - shall we not go to the park together? Isshou means together and could mean together with me or together with a group of people. A more natural sounding English translation could be - why don't we go to the park together or even - won't you go to the park (together) with me. The verb in the negative is a totally normal way of inviting someone to do something eg. Won't you eat some more? Won't you come this way? Why don't you come out with us tonight? Meaning respectively please eat some more, please come this way, please come out with us tonight.

一緒{いっしょ}に[together with me] 公園{こうえん}[park] に[location marker] 行{い}き[go] ませんか[won't you?]。

In answer to your second question it could be translated as aren't you going to the park with someone, but in the absence of a specied person or group to go together with it's always assumed that the speaker is asking someone to come with them. If it was an invite to accompany someone other than me (the speaker) or a group, then you'd state as much.

Right? Because when you're inviting someone you would write 行きましょう

I answered it exactly the same. Is it wrong?

So you wouldn't? Rude.

While i generally agree with you, both of those are incorrect for this phrase.

一緒に公園に行きませんか？ (kanji added, since こうえん is also a lecture, for instance) is interpreted as "Won't you go to the park with me?" since it's a question presented in a negative form.

"Shall we" is ----行きましょうか？ the -Mashouka? ending expresses an invitation explicitly.

"Should we" is expressed less formally than "Shall we", something along the lines of 公園に行こうか？

I think that'd specifically be 行きましょうか rather than 行きませんか

I think why don't we go to the park is closer cos it retains the negative. Or won't you come to park with me?

It's technically correct. It's just whoever designed the question put what English speakers would normally ask instead of the actual meaning.

It's incorrect because it's translated wrong, though that being said, duolingo deals with rather strict translations, "you" isn't defined and neither is "like", but both are implied. I mean neither in english do you just ask air "Won't we go to the park together?", unless you say "Won't you go to the park with me", which is an entirely different phrase.

report it

行きます is specifically to go or travel to somewhere. A leisurely stroll would be さんぽします. I feel like you might use を or で instead of に too, but I'm not sure. I usually think of に as 'to'.

Neither "you", "like" or "walk" is defined in the sentence. Duolingo is relatively strict in translations.

私と一緒に公園に来たいですか？should work, even if it is semantically a bit of an odd construct and doesn't really work honestly.

私と一緒に = [Me with together]
公園に = [To the park] 来たい = [To come] ですか？= [Question, polite]

The main problem here is the word "To come", since it's a movement action and implies that the speaker is already there, and yet you have included yourself in the sentence with "me" and "us". You could use this sentence when calling over someone to the park, but you would have to drop both "me" and "us":

あなたに公園に来たいですか ?

I agree. "together with me" is not just clumsy though - it is English that no one would ever say. You would use one or the other - you would say either with me or together, but never both.

You clearly aren't a native english speaker. "Do you want to go to the park together" is a perfectly functional and fluid phrase. "...together with me" is, firstly, needless, and secondly clumsy. "Together", when posing a question on the situation already defines "with me", just adding word padding does not make it better or worse.

一緒に specifically means "together", your whole confusion comes from misunderstanding the word and trying to tie it 1:1 with the english construct.

You should not add or remove words. You are not interpreting, you are learning, and that means you'll translate. Certain concepts and idioms may appear "strange" or archaic in translation, but the whole point is to understand what is written, not what the intention was... that comes much later.

Yes.

report it

report it, it's right

You are correct, though i'd personally use "Won't you...?"

The bigger problem with this translation is that you used the "to want to go" constuction of a verb phrase instead of the more simple and direct "to go"; it's a question of desire of an action as opposed to the action itself. 行きませんか is "don't/won't you (do you not/will you not) go". To instead say "don't you (do you not) want to go", you have to use 行きたいですか.

Should implies a certain level of obligation. 'Won't you' is indirectly asking the listener something - if you were to ask directly "will you" it would be bolder and up front. The negative verb makes the speaker's question/invitation indirect and therefor humbler and gentler than a more directly worded question.

There is a difference between "Shouldn't" and "Wouldn't", "should/shall" is more formal and has different implications as "Would". ませんか？is most definately in the "Wouldn't?" category.

一緒に公園に行きますか? - Positive question form, your answer.

一緒に公園に行きませんか? - Negative question form.

oh not twice. i mean 'negative word' + '?' = right

While your english is a bit loose, you are correct. It is a negative (masen) question "Won't" is the correct translation.

"Shouldn't we go to the...?" is too formal for this translation. The question is on the level of "Won't we go to the...?"

来ます - to come - moving towards a point
行きす - to go - moving away from a point