You can find many great websites that have downloads of many emulators (including the DS) and they usually update them so you don't have to worry about getting the wrong, old model. The emulator-zone is a good place for your emulator needs.
You cannot put emulators on the DS itself, but you have to install them on your PC.
There are lots of sites for DS emulators, and these will let you play DS games without having a DS. Emulators are sometimes referred to as ROMs.
The Internet
any DS emulators you can find
You can't sorry.
there are lots of different types of ds emulators for computer for example 'No GBA' but it isn't that good you can just go on google and type in 'ds emulator and just try some.
On a ds
propabaly not seeing as most emulators play gamnes as a singular console with no connection. you MAY be able to use netplay like wifi but i am not sure as i have not got experience with a ds emulator; i have with similer older emulators though
very few games actually work with ds emulators because the emulators are all still under development(none are full versions yet). if you want to play it badly enough get a flashplayer for your ds and have at it http://www.nintendo-ds-roms.com/
No, they cannot.
you can find ds emulators and game files on coolrom.com
Reviews for Nintendo DS Emulators for the PC can be found at The Emulator Zone forum or Gameyum. These website provide detailed and insightful comments and comparisons between the top emulators available for the PC.