HeHe and HaHa aren't really words, they are just a phonetic spelling of how some people laugh. In a similar way to how Moo! is used to represent the sound that a cow makes or woof the ound that a dog makes. This is way you will see HeHe or HeHeHeHeHe to show that you were laughing longer.

No. It means the person who typed it was laughing. It is not an actual word, but it is intended to depict the sound made when laughing.

Sometimes it means that what you said previously was meant as a joke or "tongue in cheek"

No. It means the person who typed it was laughing. It is not an actual word, but it is intended to depict the sound made when laughing.