Expressing knowledge or skill: 认识 vs 会 vs 知道
會 indicates ability. 認識 emphasises recognition (exposure). 知道 emphasises the possession of knowledge. Let us look at the following unfortunately similar examples:

i. 你會這首歌嗎？
ii. 你認識這首歌嗎？
iii. 你知道這首歌嗎？

Sentence i.: this inclines to mean 'Can you sing this song?' (There is understandably the omitted verb 'to sing') Of course by being able to sing you possess the knowledge (知道) about the song, but this sentence emphasises whether you have the ability to sing it.
Sentence ii.: this inclines to mean 'Do you recognise this song?' That is to say, the asker expects the recipient to have already been exposed to this song elsewhere.
Sentence iii.: this inclines to mean 'Do you have knowledge about this song?' There is no emphasis on prior exposure (of course by being knowledgeable on something, logically, one has to be exposed to it, but this is not the emphasis of the verb 知道 per se), the asker is simply interested to know if the recipient knows or understands the existence of the song (in this case, it functions similarly to 認識), or the content of the song. Or even the knowledge of the singer / composer / lyricist. That is to say, 知道 has the broadest and most general sense and is expectedly used most frequently in modern Chinese.

In the case of people (Dr Sun Yat-sen in the following examples):

i. *你會孫中山嗎？ / *你會認識/知道孫中山嗎？
ii. 你認識孫中山嗎？
iii. 你知道孫中山嗎？

會 functions best when prefixing a skill (游泳 'swimming', 唱歌 'singing', 寫作 'writing'). There is no possible verb candidate (not even 認識 or 知道 because they are not exactly skills) in sentence i.
The word 認識 has also developed to mean 'to know each other' (相識) over time. So unless you are a contemporary of Dr Sun or a time traveller, sentence ii. usually does not make any sense. That is to say, it is nonsensical but not ungrammatical. (Of course, you may argue there is some sense in a pedagogical setting – when asking if students recognise this historical figure based on the assumption of prior learning exposure. But in general, this sentence is slightly odd.)
Sentence iii. merely asks if you are knowledgeable about Dr Sun Yat-sen (not the other way around, the asker is not interested in that). His existence, his life etc. That is why it emphasises unilateral knowledge, as mentioned in this answer.

Finally,

i. 你們認識嗎？
ii. 你們知道嗎？

Sentence i. means 'Do you two know each other?'. The omitted object is ‘each other’ (對方/彼此). Because of expected mutuality, you can only use sentence i.
Because of unilaterality of 知道, sentence ii. cannot be used to say 'Do you two know each other?'. It only means rhetorically 'Did you two know?', the omitted object being something else.