Is it permissible to fill up water for נעגל וואסער or any other water for נטילת ידים in a bathroom sink, meaning not to wash my hands in the bathroom? If yes is it a לכתחילה or a בדיעבד?
Yes, there is no problem in filling the water for neigel vaser in a bathroom sink, and this can be done lechatchilah.
Although some write that one should not take food and drink into a bathroom (with a toilet), this is because it is disrespectful to do so (see Magen Avraham 166:3; Tzitz Eliezer 14:2; Be’er Moshe 5:1; Har Tzvi 1:50). The food, however, does not become prohibited for consumption. In the same vein, the water that one fills in a bathroom is fit for use for netilas yadayim.