I also have the Lumix TZ4 for a few days now and am really happy with it! Though the last days I couldn't stop trying out all the different settings on all kinds of objects and light situations...
Coming to your questions, Flashlights unfortunately have many undesireable side effects.
The best solution is to supress the flashlight and either use an external light source (e.g. a lamp) which would also resolve the display problem, or to use a longer shutter speed (if you can ensure the camera and the photographed object stay complety still for a second, also use the selftimer). You can also experiment with the ISO sensitivity, but this might reduce picture quality.
The whiteness of the wall can also be because of the flashlight reflecting from it, to reduce this a little, try in the manual mode (when the wheel is turned to the camera symbol) pushing the ^ button (the one above the menue button) and then changing the lightning (-2 to +2). If you choose +2, the display will be brighter, but the wall might become even whiter than before (actually better used for black object with little reflection). Selecting -2 will reduce the reflection effect and give more natural colors to flash-pictures, but unfortunately, the display will be very dark...
To reduce the display problem: there is a LCD mode which brightens up the display, though it won't be exactly the same light as the result picture.
The best thing would be a photo studio with huge spotlights
Have fun taking pictures!