The use of ありがとう and ありがとうございます is based on the person you're saying it to. E.g when receiving handouts/worksheets from my sensei, do I say 'arigatou' or 'arigatou gozaimasu'? Or is 'domo' okay? →When reciveing from teachers,it's better to say ありがとうございます.Umm,どうも is also ok,but it's even better to use ありがとうございます to teachers. Another one, when the class has ended and I am leaving my class, do I say 'arigatou gozaimasu' or 'arigatou gozaimashita' to my sensei? →ありがとうございました(past tense) is right,because the class is already finished.

"Arigatou" can only be used in casual settings, while "arigatougozaimasu/mashita" can be used in BOTH casual and formal settings. "Arigatougozaimasu" in a casual setting is used when you truly appreciate what someone has done for you, especially when that someone is an elder to whom you usually speak casually with. For instance, I don't speak formally to my mom or my grandma, but if they do something that I truly appreciate, to show ultimate gratitude, I say, "arigatougozaimasu." However, I probably wouldn't use this with my friends. "Domo" alone is a pretty casual term. It can be used interchangeably with "arigatougozaimasu" in casual settings. But in formal settings, if you want to show ultimate gratitude, you can say, "Domo arigatougozaimasu." As for "masu" vs "mashita," the latter is past tense, so you would use it when you want to show appreciation for something that's already been done!!