Korean and Japanese are likely related (at their root, the way english and say dutch are related) but this is debated and highly political. They have a similar grammatical structure and are thought by some to be both related to Altaic languages such as Mongolian and Manchu. Chinese is in a different family of languages, and although they are know as "hua" or "dialect" in China, different variants of Chinese are at least as different as separate European languages. Mandarin, Hokkien, Cantonese, Shanghainese and other Han languages have a similar grammatical structure, pronouncedly different from Japanese and Korean, and are more closely related to Tibetan and Burmese. Now, this is all complicated however by loanwords moving from Chinese to Korean and Japanese (as well as Vietnamese which is in another language family again and related to Khmer and Malay). This is similar to words in English taken from French and Latin, such as "information", "severe" or "equality". Again this is complicated by the fact that those words come from multiple Chinese languages at multiple points in history. At the end of the day, some words sound similar such as "partake" - "sanjia" in chinese, "sanka" in Japanese, "prepare" - "zhunbei" in Chinese, "junbi" in Japanese, and "cheers" - "kanpai" in Japanese, "gunbae" in Korean, and "ganbei" in Chinese. But these are separate languages like Greek, Spanish, and French are, they are fundamentally mutually unintelligible.

Well first off Korean is an isolate language, so it is not related to any other language in the entire world. It did I think borrow some Chinese (Mandarin) writing characters, but that's about the only similarity. Chinese (Mandarin) and Japanese from what I know are mutually unintelligble (ie speakers from either language cannot understand each other). Japanese did adopt many Chinese characters though and that is the basis for one of its 3 alphabets.

Chinese belongs to a group called Indo-Chinese languages, and is not too different from Indo-European languages.. Japanese belongs to the Japonic family, and its relation to Korean is disputed. Korean does not belong to any language family.

As far as I know, all three languages are mutually unintelligible, and Chinese is the only tonal language of the three. The situation is a bit confused from them all having a history of using Chinese characters (Korean dumped all of them), and naturally borrowing words from each other as neighbouring languages.