How do I get into Garrett's house?
Try inspecting the houses around the one Garrett lives in.
There are several ways into the house, and I list some of them here.
Check the streets around your home, and look out for doors. There is a storehouse (not the house with the sleeping woman, the other one) that has in its 2nd floor a window facing the front entrance of Garretts home. From there, you can see a window with closed wooden shutters. This is the window of Garrett's sleeping room. When you hop across the street, you are on the windowsill, and the wooden shutters open to the inside.
At the backside of the house is a wooden kind-of fireladder. You had 5 rope arrows in your inventory when you started, and I hope you've still some left... the small window leads into the staircases of the house, take care a bit there, because there's a Guard on patrol.
The main entrance may not be the most stylish way in, but it also works, when you use the "lean forward"-trick for blackjacking.
How do I get into the graveyard?
Don't bother. You are not meant to get there in this mission, and there is about nothing to see there, and definitely nothing of worth... okay, you can have some fun there, but it is a one-way adventure anyway.
Still not convinced that it is not very funny in there? Okay, -but don't blame me when you accidentally overwrote your last save when you are in the graveyard- first of get rid of everyone who could get into your way in the NE area of the Marketplace. Then, you need a barrel and two crates (or you need to find a secret hideout of about a dozen crates, if you dislike barrels). Two crates are i.e. behind Garrett's home, and two other crates are in the area S Helena way. Barrels can be found in the S of the Marketplace. Get your stacking utensils to the E gate to the graveyard (reacheable easiest via the NE exit of the Marketplace). Build a nice stack of 2 crates at the top of a barrel, close to the wall with the gate, of course. Take a real save, now, because it is a one-way adventure. Mantle on the wall, and hop down the other side.
In this level, I have pulled a lever in a brightly lit room with a little table and chair (if i recall correctly) and can hear a gate opening. Where is this gate and how do I get there?
"Right below this place." (The gate that opens is right below the room with the lever, and it is heavily guarded.)
What happens if i don't pull the lever?
If you don't pull the lever, the gate doesn't open.