-Can the DS play downloaded games or hackable games?Do all DS require original game cartridges?
The DS by itself cannot. You will have to get a R4 or any other similar cartridges which allows you to play downloaded roms on your DS.
-Sequence by size and weight?
No idea for weight. But DS Lite is the smaller version of DS whereas DSi is the newer version DS with a camera, but is unable to play GBA Cartridges.
-What items are necessary to play/start-up the DS?(battery,game cartridge?)
Battery comes with the DS. Its unlike the old game boy where you use AA batteries. Kinda like your handphone. You will of course need a cartridge to play.
-How many of each items are needed?
If you are going original then you will need cartridges of games you wanna play. If you get a R4, you'll just need the R4 and put the games in it.
-Important items needed to keep the DS in good shape?
probably casing and screen protector