Hi,
Well,
1. The quality of the result depends on the quality of the scan doubler, whose role is to change the PAL/NTSC video signal into a VGA signal displayable on a LCD. My only experience with LCD TV is the Samsung 2032MW I'm talking about in this thread. In my opinion, its scan-doubler is too bad for anything else than watching movies/television and word processing. So if you want your Amiga to look like an Amiga, then you have two solutions : either finding a better TV, or use a good external scan doubler between your Amiga and the monitor (in that case the monitor must meet the requirements of the scan doubler instead of the Amiga). Hodgkinson has just showed me a video that compares the Samsung to a Sony KDL-26U2000 LCD TV : although the result on the Sony is worse than on a CRT TV or monitor, it is much better than the Samsung.
2. To my knowledge, SCART is the best solution indeed. Component may be an alternative, but as I'm not a specialist somebody else should answer you. According to Hodgkinson, the SCART cable from AmigaKit will do the job. At
http://www.amiga.org/gallery/index.php?n=2449, he posted some more information. An external scan doubler may impose a particular format. In any case, don't use Composite or Aerial if you want the best quality.
3. I believe that picture quality will always be worse, unless you manage to find a perfect LCD TV, but even in that case pixel upscaling would bring you a worse result. On my Samsung, everything is bad : animation, colors and upscaling.
4. Any LCD TV will accept the default Amiga screen modes which are used in a default Workbench and most games. If you want to connect your Amiga through a VGA (D-Sub) input only, then the LCD must accept 15 KHz through the VGA input indeed. If you use an external scan-doubler, then you don't need 15 KHz, but the monitor must meet the scan doubler's other requirements.
LG monitors are probably better than my Samsung, but I cannot assure you of that.