If you ask how long ago, you would get the answers with a number and a time unit, like one year, 3 weeks, etc.
If you ask when, you would get a specific time / date.
Meanwhile you can use when to ask events happen in future.
To know someone is to be familiar with them, or to know what kind of a person they are.
You can know someone or something better, meaning to be more familiar with them, or to have a greater knowledge of them.
When someone says "You should know me better than that", that is referring to how well you appear to know them, and they are saying that they expect you to be more familiar with them. In your example, you said that the man did not seem to like you, to which he replied that you should be more familiar with him than to think that he did not like you - that is, he does like you, and he would expect you to know that.
You use this kind of phrase when someone has expressed an opinion about you that is not only wrong, but that you are surprised they would have, because you expected them to be more familiar with your character. For example,
"You think I would cheat at a friendly game of cards? Come on - you know me better than that."
(that is, the speaker is expressing surprise and dismay that someone would think that he would cheat at cards)
or
"Do we have to bring potato salad to the Johnsons' picnic too? We're already bringing dessert."
"You know me better than that...I can't bring just one dish!"
(that is, the second speaker is saying that the first speaker should know that the second speaker is not the kind of person who would bring only one dish when invited to a picnic)
Best Answer
The phrase
happen to
appears to be used in the following ways usually. When you're asking someone 'Do you happen to know this person or information?', it indicates that you believe chances are that they don't know that person or information but you're exploring the remote possibility that they might.Similarly when you're saying that you happen to know someone or some piece of information when not initially asked if you happen to know, you'd be doing it to convey that it was unexpected, but you do know.
This might help clear some aspects of the usage for you: http://www.phrasemix.com/phrases/happen-to-do-something