1) If someone drank from a cup of water can the rest be used for netilas yadayim? 2) Can a small amount of water that was used for melacha be batel in rov of kosher water and be used for netilas yadayim? Tizku Lemitzvos!
1) Yes, there is no problem in using water that was drunk from for Netilas Yadayim, and this is not considered melachah. The Gemara writes that water that was used for netilas yadayim should not be drunk, because of shichecha (causes one to forget Torah learning), but there is no problem with the reverse.
2) Water that was used for melachah includes water used for washing dishes, for processing food, and for cooling (see Shulchan Aruch, Orach Chaim 160:2-5). The Peri Megadim (160, M.Z. 5) writes in the name of Terumas Hadeshen that disqualified water is batel in a majority of kosher water, and there is no need for double the amount of kosher water. The same conclusion is reached by Chochmas Shlomo (160:1).