I think you are overthinking this.
First, I doubt the Allagans still exist in the first; it's more likely they never got there. CT's original purpose seems to be opening a rift to the Void, not enable shard hopping in general. Also, CT was at the epicenter of the great quake, so that would make it a very dangerous place to be...
Besides, we got some info on the city at the foot of the CT in the First. It was found x numbers of years after the CT appeared in the First, it's a melting pot of different races, and it's purpose is to provide shelter from the sin eaters. Nothing really screams 'Allagan city' to me.

Second, no. Definitely not. The Warriors of Darkness are from the First; and before they became the Warriors of Darkness, came to the Source and tried to kill us, they where the Warriors of Light, just like us. Therefore I would wager Hydaelyn is either unknown to the First, as she was for a very long time on the Source, or she is referred as the Mothercrystal there, too.
Besides, the "no past" thing is explained as the Devs wanting us to have the chance to flesh out our own character's background, instead of having it provided to us. Besides, we don't suddenly appear in the cart or on the shop, or the trader would have been surprised about our sudden appearance. It looks more like we got on the cart at one point, likely paid for the passage, then fell asleep and what you call 'pop into existence' was a dream we had, or at least we initially think it was.