"We are not swimming today."

Translation: हम आज नहीं तैर रहे हैं ।

[rmiller]

Do we have to include the हैं at the end. I wrote out the answer without it (because it hasn't seemed to matter) and it got marked wrong.

[vinay92]

No. Since the sentence has नहीं, हैं is optional. You can report it if you see the sentence again.

[superachu]

How to identify when to put 'नहीं' before or after?

[vinay92]

नहीं can go on either side of the main verb (तैर). Placing it before is the standard form and putting it after emphasises the negation.

[Pierre891640]

I do not understand why the process is slowing down to three point at a time. It is so boring to repeat the same sentences for hours ! Is this a bug ?

[OJFord]

Can नहीं not be moved to before हैं ? (It isn't accepted.) i.e. if literally translated 'it is not that we are swimming today' rather than 'it is that we are not swimming today'.

[vinay92]

No. The two possible placements of नहीं are before तैर and after तैर (ie, before रहे).
But note that the nuances that your two English sentences communicate by differing placements of 'not' don't come across in Hindi by changing the placement of नहीं.