Is it permissible in novels to write about a character who dreams while asleep in general, or sees something in a dream and then the same thing happens to him after he wakes up, or something similar to it?

There is no religious prohibition against writing about what a person sees in their dream if the dreamer is known for truthfulness and their story contains no falsehood. As for writing about fictional characters, scholars have differed regarding its ruling; some disliked it, while others permitted it if the objective was noble, such as teaching knowledge, calling to virtue, explaining wisdom, or if it contained moral and social benefits, provided the story does not contain any reprehensible elements or glorification of falsehood, in which case it would be forbidden.