1. I cut out any revealing parts of the players guide before I gave it to my PC's. Also do not let them see the guide to Korvosa unless you edit also -if i remember correctly there is a secrets section! regarding Lamm, depending on what happens to him in your game; I added him as a Zombie in Rolf's lair... And I have really focused on Rolf as the main antagonist in the first 2 books. Keeping the players interested by having Rolf as the real source of their coming together.
2. Edge is one big foundation laying introduction and foreshadowing exercise; use it as time for your party to get to know the city.
All the world's meat is the party's first introduction with the Arkona family. Eel's end is the party's first experience of Old Korvosa's seedy underbelly. The time going through these encounters will give you lots of NPC's and locations to bring back later in the AP.
3. I too found it hard make Book 2 a mystery to solve. My party are currently half way through it. I have planned it as the Manor encounter is the direct clue to the Doctors - not just with the crazy half elf leaking Rolf's location at the blessed maiden.
But by also having the manor's owner being the man in charge of the new mint of coins for the Queen's reign. ( I have had Amin invite the party to the manor for a VIP party (x amount of days away) at the start of the book as an insurance policy that they will go there.)
I have leaked in clues towards the coins being the source of the plague throughout the book. Rackers alley I had dead plague bodies - untouched by the ghouls- all having purses with newly minted coins in. When the party visited the bank of Abadar, Darb Tuttle mentioned in conversation that they were busy with the new mint. Giving the party opportunities to focus their investigation on the coins and possibly go to the manor earlier - rewarding them in the process by not wasting time with the boat,rats,perfume. The party has of course focused all of their efforts on the boat and rats!
I think the important thing for book 2 is to give your group options - and leads - let them decide where they go. Just don't make it too obvious that the doctors are the cause - as they are expected to experience most of the encounters in the book first.