Haiku almost never have any direct metaphors, and never have similes. On the other hand, haiku often have a juxtaposition of two images or ideas. Many times this creates a comparision with an implied suggestion of similarity.
As for rhyme: Haiku is a an old Japanese poetry form. In the japanese language there are a fairly limited number of word endings, so there are many more words with similar endings than there are in English. That is probably one of the reasons that Japanese poetry forms such as haiku, senryu, tanka, renga, etc. are not based on rhyme, but are based on morae (onji or hyouon moji in Japanese).
When people started to write haiku in English, there were some who wrote their haiku with rhyme, but most did not. Today, there are almost no English-language haiku that rhyme.
Also at that time, most English-language haiku were written in 5-7-5 syllables. Later on English-language haiku writers learned that syllables were not the same as onji. For example, London is two syllables, but four morae or onji (Lo/n/do/n/). Today, most haiku that you will find in the major English-language haiku journals (Heron's Nest, Modern Haiku, Frogpond) are usually less than 17 syllables, with an emphasis placed on brevity and conciseness.