A while ago, I asked my penpal to skype calling for the first time in a while, and she answered "I wondered if you would ever ask me"
Does it mean like, "I wondered when you would ask me that again" ?
I can just loosely understand what she says, but not completely.
I think I don't understand how to use "would ever", or could be, "ever" itself.
http://www.thefreedictionary.com/ever
According to this page, I think her message is go with 3, for emphasis. Then it could contain a sense as in, "what's taking so long?"
Learn English – How should I understand this “would ever”
meaning
Best Answer
Your interpretation is close, but not entirely correct. From your link, you actually want meaning 2. The literal meaning of your friend's response is:
However, this is almost definitely a form of exaggeration. The figurative meaning is more like what you said: i.e., "What took you so long?" It's also possible that she literally didn't know if you would ever ask her to skype again (e.g., if she thought that you had cut off all communication).
Exaggeration can be used for emphasis, among other things. I think in this case it's likely that it was for a light humorous effect at your expense, possibly being ironic (saying the opposite of what you mean) if she was actually expecting you to ask her to skype any day now.