语法Summer is the only time of year that it doesn’t rain much

1、语法正确,虽然听着很别扭（无奈啊）
2、不能省略it,因为这里it是指“天气” （如：it is raining.) 如果省略了的话就是在说 Summer doesn't rain much不合英语语法.
3、Mr Smith is the only foreigner that he knows.这句话其实也有“it” 是不过是 “he”,也是“他”的意思.我觉得你是想说这么一个例子：
Mr Smith is the only foreigner that doesn't speak a foreign language.
这里因为前后主语相同 （Mr.Smith既是 ...is the only foreigner 的主语,又是 .doesn't speak a foreign language的主语）,所以不需要it,he,she,they之类的东西.
总结：当前后主语一样时,that后面何以直接跟动词（省略主语重复）,不一样时,that后面必须是重伸主语的完整句子.