"The woman does not swim towards us."
Translation:Ní snámhann an bhean chugainn.
The verb should be ní shnámhann ... need lenition for a negative statement. (I've reported this as an error - just sharing for the benefit of any other confused course comrades.)
No. Níl is only the negative form of bí in the present non-habitual. It's actually a shortening of ní fhuil. Ní is used to mark negativity in most tenses.