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No, GBC saved games are saved onto the the game cartridge itself.
cartridge
Data is saved on the cartridge itself. It doesn't matter what system the cartridge is played on - no user data is stored on the console, except wi-fi settings.
If the game doesn't have a menu option to do so, or in the case of the Pokemon games, a specific set of keypresses described in the manual, then there's no real way to 'delete' the saved games, apart from overwriting them with newly started games.
Some games that need more graphical memory such as Donkey Kong 64 or Majoras Mask need the Expansion Pack. A few games need to be saved to the N64 Controller Pack. Just search each game and you will know.
You cannot have more than one saved game per Pokemon Ruby game cartridge. There can only be one saved game per cartridge.
Yes all game data will be saved to the Cartridge.
Cartridge and disk video games are simply two styles of storing the game (mostly old and new) sort of like floppies verses CDs for computers. A cartridge is mostly the older way of storing a game for example a lot of the first video games for game systems were on cartridges, which were plastic blocks with the important hardware inside them and one side was open where it was fitted into the system. With cartridge games the saved game data was usually stored on the cartridge it's self. Cartridge games still exist to an extent though they are much smaller for example the game boy SP and advanced games could be considered cartridge games though I am unsure whether DS is quite a cartridge game, older examples are the N64 and most older game systems. Disk video games are exactly what they sound like the game is stored on a disk (similar to a CD or DVD though usually a different size etc), with disk video games the player's saved data is usually saved on a separate memory card. Disk games are much more common now especially with game systems you hook into the tv as oppose to handhelds, for example Game Cubes, Wiis, Playstations, etc.
The data is saved onto the cartridge. Remember that the DS and DS lite do not have internal memory.
Yes, data like DSiWare games and pictures can be saved onto an SD card.
Yes, saved game data goes directly onto the game cartridge, rather than the SD card.
Sounds like a savegame manager like AR Max Duo or Gameshark/Xploder. You can copy saved games to and from a DS game cartridge and store them on PC.