TO "Deal with Lady Elizabeth" and her 2 thugs you don't have to kill anyone or even be seen. Instead, sneak into the crawlspace under the stairs near the fountain. You'll be in a city watch building, but it's empty today. There are two sacks of money on a table in one of the rooms. Grab them both and hide. If you want entertainment, hide in yourcrawlspace, and Elizabeth will come in with one of the thugs, and notice the money missing. Thug will threaten her, and she'll kill him. The other thug will enter and kill Elizabeth. Then, you can make your getaway
Although shadows are important to hide Garrett, sometimes it can too dark to see while hiding. Crank up the Gamma/Brightness correction in your options menu to see the surroundings while remaining hidden.
This requires a bit of code editing, so do the smart thing and BACK UP YOUR FILE.
Now, that being said, you'll want to find the Thief 3 directory and go to the System Folder. (Default is: C:\Program Files\Thief - Deadly Shadows\System). Look for default.cfg. Open up this file in your normal text editor and look for this:
-- THIEF 3
AI visual acuity multiplier - how well AIs can see
AI auditory acuity multiplier - how well AIs can hear
AI tactile acuity multiplier - how well AIs can feel
AI hitpoints multiplier - all AI starting hitpoints will be scaled by this
AI combat speed multiplier - all AI combat animations are scaled by this
AI-to-player damage multiplier - all damage applied to the player by the AI is scaled by this
The higher the number, the better they see, the harder they hit, faster they are, etc. Edit the numbers to your liking, start a new game and enjoy.