I am not sure that I understand your intentions, but if your employer removes the contribution from the HSA by contacting the HSA custodian directly, then any corrected W-2 will have the code W amount removed. This means that TurboTax won't know that you have an HSA, and you will not indicate that you have an HSA in the "Tell us about your health accounts" screen.
At the same time, if the employer had previously removed the code W amount from Wages in boxes 1, 3, and 5 (as they should have), I imagine that they will add the Code W amount back to Wages in those boxes. I am not sure what your employer intends to do about the dollars that were supposed to go to the HSA which now have been withdrawn. With these dollars be distributed to you? I don't know.
As for being taxed twice, that should not happen because, as I said, if the employer removes the $2,500 from the HSA themselves, then the employer should also remove the Code W code and amount. In this case, if you follow what I said above, you would not even report an HSA, so TurboTax will not add back anything. What your employer does with Wages is unknown to me (see paragraph above).
As for your last questions. I will repeat my final statement previously:
As for the issue you are having with TurboTax demanding an answer of Self or Family in the Review, it would be OK to answer either, because you have already told TurboTax that you did not have any HDHP coverage, so all the numbers on the 8889 are correct. Answering Self or Family is just to get around this issue in the Review that holds you up.
And you won't have to click NONE per month, because TurboTax will ask you first if you had any HDHP coverage at all, to which you will answer No. Then you will never see the month by month screen.
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