When washing hands, which hand needs to be washed first, when waking up, before bread, and after toilet respectively?
Are there different opinions in it?
Mishnah Berurah 4:9 for Netilat Yadayim in the morning
One should wash one's right hand first, then one's left hand, and repeat this process two more times so that one washes each hand three times, while alternating hands in the process. Some say one should wash each hand four times.
To wash netilat yadayim for a bread meal one should pour water on one's right hand three times and then pour water on one's left hand three times.
Upon leaving the bathroom, “Many poskim hold no kli is necessary and neither is washing three times.” Mekoros:
https://www.ou.org/torah/machshava/tzarich-iyun/tzarich_iyun_washing_after_leaving_the_washroom/ quoting Yalkut Yosef v. 3 p. 96. He points out that there is a stringency to wash with a kli outside the bathroom but washing with a kli in the bathroom is pointless. Rav Ben Tzion Abba Shaul (Ohr LeTzion 2:1:15) held that a keli is nice lechatechilah but not necessary MeIkar HaDin; however, three times is always necessary. Rav Ovadia (Yabia Omer 9 OC 108 fn 4) lightens some of his arguments by noting how one cannot compare this to washing in the morning. Rav Mordechai Lebhar (Magen Avot Orach Chaim 4:18) quotes Rav Shalom Meshash (Shemesh uMagen vol. 3 Siman 37) as reporting that the custom in Morocco was always to wash once at the sink without a kli according to the simple reading of Shulchan Aruch that a kli is only necessary for the morning washing