Yesterday my brother cut himself with a knife.
2) Don't burn yourself. Don't hurt yourself. Don't cut yourself
3) She was going to go to the party and looked on herself in the mirror
4) She never speaks with herself
5) Предложение написано непонятно и плохо, так как единственный нормальный вариант на русском будет звучать "у меня нет на себя времени", а не у меня нет времени, так что - i don't have any time for myself, и так и скажи что построено предложение слишком криво, другой бы и не понял.
Wash the plates by yourself
6) Тоже довольно странно звучит, но раз уж надо по заданию.... I hope himself will have fun from the spectacle.
7) Тоже. I hope yourself will have fun from the spectacle
8) Тут все нормально. Goodbye, look after yourself and come back soon.
9) I don't like him because he thinks only about himself.
10) Sorry, i can not explain you this rule, i don't understand it by myself