Generally speaking, 3 beeps indicates that there are no good banks of memory. This could be due to disconnect, faulty modules, or a faulty logic board. Best case scenario is that you pull and reseat the memory, and it works fine. Next test each memory stick individually. If that doesn't work try and get your hands on a set of knowing working memory and test again. If that doesn't work, you need a new logic board.
You are correct, it uses a PATA connection, and in order to use a modern (half decent) drive, you would need to convert the connection from a PATA to a SATA drive. Of course these are still IDE connections, just different interfaces given the project. A convertor like this would work: http://firmtek.stores.yahoo.net/seritek1... The issue is then compatibility. To be honest, I know that Apple has never truly supported PATA to SATA connections, but that doesn't mean that it won't work.
The best method for installation would be to create a USB boot disk using your Snow Leopard DVD. Put the DVD into the drive, insert a USB disk drive that is at least 8GB, and then "burn" the image from the DVD to the disk drive. Boot your system and hold down "Option" key, select the SL disk and continue on.
It may be the cable, the inverter board, or the LCD panel itself. Until you start to rule out each one there isn't really any way of knowing. Unless of course there is physical damage to the panel. Once you take the LCD panel off remove the bezel, then remove the clutch cover, the cable is the black one on the left, and the inverter is in the middle. Try the cable first, and check all connections. If that doesn't work, try the board. If that doesn't work, then you know that you need a new panel.
If it is cracked it needs to be replaced. Does Apple do it? Yes, will it be covered? It depends greatly on the situation, but generally physical dage is not covered under any warranty. If it isn't they will quote you a repair cost. If you are patient and willing repairing it your self is also an option.
This is somewhat normal, but it depends on the environment and surroundings, as well as the rest of the computer (what you are running). I would recommend that you change the buffer of YouTube, you can do this by right clicking on a Flash video and selecting "Settings". Then deselect "Enable Hardware Acceleration" on the first tab, and set the third tab scroll bar to 10MB. The bottom line is that flash is very, very demanding. Hopefully those settings help a bit though.