the precious character means you are skillful at certain things, eg. 我会唱歌，I can sing. It's referring to abilities. The latter one is more likely to express that one understands or is aware of something, eg.我知道你，i know you. its a knowledge thing.

From my understanding 会 as more on your ability, and 知道 is your knowledge Your first example says I know how to speak Chinese, while the second is I don't know. I think that 知道 is usually used to say whether you know or do know something/someone. I thing that it is used with nouns. You can't say 我知道游泳 (I know how to swim because it will be grammatically incorrect). However, 会 can be used. 我会游泳, meaning I know how to swim/I am able to swim. Unlike 知道, 会 is used for verbs. My textbook has a lot of texts, so I just picked up when it sounds wrong/right so this is what I figured out. It should be easy to tell when to use hui or zhidao. But, there is another one that may confuse you, which is 能. It is used like 会, but there's a different rule that comes with it.

I can speak Chinese (Mandarin). I do not know.

How about this sentence: 你知道我会唱歌，吧

In my opinion, to be simple, 会 means you know how, 知道 means you got it, or you know why.