Давайте рассмотрим каждое предложение и исправим ошибки, если они есть:
I hope that next time you'll speak to your uncle more politely. (Правильно)
Peter usually comes to his classes later than most of his classmates. (Исправлено "most late" на "later than")
Who can solve this problem most quickly? (Правильно)
This time he listened to his little sister more patiently than usual. (Исправлено "patienter" на "more patiently")
Could you speak a little slower, please? (Исправлено "Cold" на "Could")
When I was a very young child I thought that to sing best meant to sing loudest. (Правильно)
I think that now I see the whole problem much more clearly. (Правильно)
Who lives closer to the school - you or your friend? (Исправлено "more near" на "closer")
Alice goes to the theatre most frequently of us all. (Исправлено "frequentest" на "most frequently")
Will you raise your hands a bit higher, please? I can't see them. (Правильно)
In December it snows more often than in November. (Исправлено "oftener" на "more often")
Таким образом, предложения 1, 3, 6, 7, 10 уже были составлены верно. Всё остальное требует исправления.