May one wash his hands after using the bathroom and after other impurities using the bathroom sink?[1]
One who uses the bathroom [or does other actions which requires him to wash hands afterwards in order to get rid of the evil spirit that resides on his hands] is to avoid washing his hands using the water of a bathroom.[2] This applies even if he takes the water outside the bathroom.[3] However, in a time of need one may wash his hands inside a bathroom, and may certainly remove the water from the bathroom to wash outside.[4] This especially applies to the sink of a public bathroom, which is generally in a separate area of the room than the toilets and urinals.[5] Nevertheless, initially one is to dry the hands outside the bathroom.[6]
[1] Os Chaim 43:1; Kaf Hachaim 4:11; Y.D. 116:73; Minchas Yitzchak 4:37; Chelkas Yaakov 2:162; Yabia Omer 9:108; Piskeiy Teshuvos 4:19
Background: Although there is no prohibition in doing a Mitzvah within a bathroom [Darkei Teshuvah Yoreh Deah 19:21] nevertheless the question is raised whether the water in a bathroom is able to purify one’s hands. The Kaf Hachaim ibid differentiates between using the bathroom washing water for washing after use of the bathroom, which is permitted in a time of need, versus for washing in the morning after awakening, or for bread, in which case you say a blessing over it, and it is more stringent and the water is invalid. However, it is unclear if this invalidation is even with sink water or only with toilet water. See Devar Yehoshua 1:76; Piskeiy Teshuvos 160:19 footnote 73 who learns that it only applies to water that stayed in the bathroom for a while, and not to sink water
[2] Zechor Leavraham 3:49 and Zivcheiy Tzedek 2:116, brought in Kaf Hachaim 4:11 and 116:73, that so is the custom of the masses to spill out the water that they brought into the bathroom for washing purposes and they do not wash their hands with it even for the sake of washing hands after using the bathroom; Minchas Yitzchak 4:37
The reason: As a bathroom is a place of impurity and hence how can washing in it remove the impurity. [Minchas Yitzchak ibid in name of Poskim]
[3] Har Tzevi 1:50; Devar Yehoshua 1:76; Vayaan Yosef 1:2; Piskeiy Teshuvos 4:19; 160:19; 171:9
[4] Zechor Leavraham ibid; Os Chaim 43:1; Kaf Hachaim ibid; Piskeiy Teshuvos 4:19
[5] See Mishneh Halachos 5:2
[6] See Yabia Omer 3:1; Chazon Ish 24:26; Vayaan Dovid 1:1; Az Nidbaru 14:86; Piskeiy Teshuvos 4 footnote 192