That's not a compulsion to visit, that's his Sight. Anastasia explained that one to him at the end of the book, it's a deja vu effect that Wizards experience.
Remember the quote you yourself posted, Alfred has no power, no existence, nothing, beyond the bounds of the prison. We don't know if the cutoff point is the shore or just precisely where, but it's close to the island anyway. JB himself once described Alfred's power as being a matter of one's GPS coordinates.
I was quoting from the book, which is all I have to go by. I think JB may have fudged on that last point. In Battle Ground, though Alfred could go as far as Chicago to gather up the Titian, Alfred could only do that because of Harry ordering it. It said itself I believe that it could do nothing beyond the shores of the island without Harry. I have to go back and reread that part, so not positive on it. However I remember something about Harry asking Alfred why it just couldn't go and get her.
Yes, I am aware of what Luccio said about the sight, and I may have not been clear enough. Harry ended up on the island in the first place to save Ivy and Marcone in Small Favor, then he felt that he had been there before. This led later on in Turn Coat Harry asking Morgan questions about the island, which led him to believe it was the safest place to confront the Senior Council over Morgan. That's where the idea came to him to perform the sanctum thing with the island.. So if other powers influence future Wardens to come to this island, I guess you could say Nic of the Denarians and the Warden, Morgan are it. I think it unlikely that Nic did it, unless of course he thought because Harry would have Lasciel in his head, that in the future as Warden of Demonreach Harry could be of value to the Denarians.. It is possible if Morgan knew about the prison or what the island was, he thought Harry would make a good Warden, but I also think that unlikely. I think if Rashid and Eb were a bit shocked that Harry could pull it off, I doubt that Morgan would believe given the consequences of the sanctum would think that Harry could pull it off.
So your quote and that one both support the idea that Alfred is powerless beyond the island.
That doesn't mean somebody didn't arrange for Harry to meet Alfred, just that it almost certainly wasn't Alfred.
It doesn't, but at the same time very unlikely, because in the same chapter Harry says that Alfred spoke to him in Ghost Story when Harry was hanging out in his grave. Alfred answered that he had bargained with Mab to be able to do that, otherwise he couldn't and hadn't ever spoken to him or left the island.
Incidentally, I don't know if JB intended this or not, but the name 'Alfred' might be ironic. We've seen that the Faerie royal mantles have some kind of influence over him, and the name 'Alf-red' is cognate with 'elf', IIANM.
Possible, but I think it's more of an unintended coincidence, I think it is what it appears to be, Harry calling it Alfred after Batman's faithful butler and keeper of the secrets of the Batcave.