To answer the question on the wires my brother in law installs these things often for customers and he gives them three options:
1) If it's the right type of wall: Make a hole in the wall, insert a little plastic tube and run the tube down in the gap between the wall and the "stud wall". Then run the cables through the tube. Then repair the wall.
2) If you can't make a hole on wall, run the cables on the outside of the wall and hide them with a unit/similar.
3) Again if you can't make a hole on the wall then attach a box section tube to the outside of the wall and run the cables through that. I believe they call them "cable raceways" or something like that in the US. Looks like this:
As to your questions on picture quality, this is my (limited) understanding which I hope is of use. You have three type of signal available to you:
1) Analog
2) Digital
3) Digital HD (High Definition)
The short answer is without looking at your setup I can't tell which one you have. The likelihood however is that you don't have an HD package. If you don't then it comes down to what connectors you have on your box as most cable/satelite TV today is transmitted digitally.
If you have a SCART cable, that looks like the picture here, then you are transmitting an analog signal to your TV:
The same thing if you have a standard connector (I forget the name), that looks like this:
In those two cases your picture MAY look better with a flat screen but it's not certain. The SCART is capable of decent images (notably from DVD players) but mostly it will look the same as a "normal" tube TV. The reason is that a standard TV signal "compresses" the signal. When you put this up on a big screen, the TV "fills in" the gaps. Tube TVs "fill in" differently than LCD/Plasma TVs. In essence the tube tv does it less well in theory but because the signal is rubbish to begin with the whole thing looks smoother. The digital TV does it more accurately but essentially "exposes" the flaws in the signal much better. Ironically this means you get a less good looking overall picture. From a DVD the flat screen should look better (better start signal), from a cable box it's a 50/50 shot dependent on how they compress their feed, their source quality etc..etc...
I'm limited to 4 images so I'm going to continue in the next post