Can all of my devices on my Apple ID account see all my messages on imessage?

Yes, he does.

I just don't understand why this works only if a conversation exists, and as I said above, how does a conversation start and be shown on the iPad?

As I say, this is one area I'm not all that sure about myself. Is it not possible that these conversations have actually been started from the iPad or from your Mac.

Yep, that's likely. I've just started a conversation on my iPad to a phone number, and it certainly works.

I think all this needs to be made clearer in future versions.