Those are fine, but "May is in a month" should not be the preferred translation. It is unnatural. If I heard a non-native English speaker say "May is in a month", I would try to suggest alternatives to obtain the intended meaning. This point has more relevance for those learning English.
I say this all the time and I am a native speaker. It might be something that people just have variance on in English. I will ask the other native speaker on our team about this. :) (Also, if it were April 1st, it is definitely a perfectly good sentence for everyone, right?)
I don't find "May is in a month" all that unnatural either, not in colloquially spoken English anyway. If I were writing something formal, I'd probably use other choices of words, but in everyday speech, I think many would find it acceptable.
This discussion made me curious about whether or not "in a month" was used more frequently than "a month away," so I decided to check it out on Google Ngram and was actually surprised to see the following:
I then did the same search of Google pages and found that "in a month" was more frequently used than "a month away" there, too, and by even wider margins than what you see in the Ngram viewer.
It is really interesting to compare the language you use and how those in your immediate circle use it with what is seen via Google finds. Sometimes what you previously thought wasn't all that common is more common than you had thought and vice versa.
You are thinking of Turkish phrasing and translating word by word but I'm afraid it doesn't work correctly in that way. It makes it sound very Turkish but only with English words. :)
The way to say "bir ay sonra" is done by using "in a month". For example "doktor randevum bir ay sonra" is "my doctor's appointment is in a month". Using after makes it sound as if you're saying "mayıs bir aydan sonra" which is confusing and wrong.
Does this help?
Please can you be specific? Is my reply above to the learner wrong? Your Turkish wife must be able to explain if Duo's or my answer is wrong by giving an example here.
She is "shoulder surfing" you while you are learning Turkish on Duo.
Ask her to correspond here with me in Turkish/English please? Everyone will benefit from positive feedback.