No, WiiWare games are only playable on the Wii (and Wii U) so the DSi cannot play it.
No ... by games I think you mean dsi roms the only way to play dsi roms is by using a flashcart as nintendo thought about this and they blocked playing by your memory cardor internal storage
The DSi can't execute code on the SD card, all it can do is store pictures on it, or play music. There's no way to play a homebrew game off the SD card, the DSi simply wasn't made with the means to do so.
That is not possible. You can transfer DSiWare games from DSi to 3DS, but not the other way around.
No, simply because the action replay was built for DS games. You can't play 3DS games on a DSi anyways because the software that the DSi runs won't read the newer chips. Also, the 3DS chips won't fit into a DSi because of the way that the 3DS chip was designed. However, the DS games can be played on a 3DS because the newer systems can recognize the older games, you just can't use the 3D feature.
No, the Nintendo DSi cannot play GameBoy Advanced or GameBoy Games. However, it can play all the games for Nintendo DS Lite and Nintendo DS, except for games that require the slot 2 such as Guitar Hero.
If it's a cartridge game, you insert it into the slot at the top of the DSi. When you switch the DSi on, the game will be shown on the menu bar, select it or touch it with the stylus to play. If it's something downloaded from the DSi store, it too will be on the menu, further to the right. Just select it in the same way as above.
in your poket or cabnits
The only way to get a video feed like that is a hard modification of the console itself, inserting a card containing a USB port into the circuits of the display. There is no way to 'plug something in' to the DSi to do this, none of the DSi's other ports have any link to the visual feed.
You are suppose to go to dsi settings then go to data management and copy the game you want ( it must be downloaded from the Nintendo dsi shop) then you should be done, but it is much harder. It is almost impossible to copy it to a different dsi. This trick doesn't work any more so I erased it' I hope you find a way to copy your games to another dsi. :) :) :) :) :)
Yep, just not GBA/GBC/GB games from cartridges. There is going to be a DSI shop for buying previous GameBoy games, but that's just a way for Nintendo to make money form old games without any real expenses
No just the same way as a DS Lite !!
Resetting a DSi will have wiped anything you put on it. There's no way to get them back. If you mean DSi Store games, you can just redownload them from the DSi Store, deleting them doesn't mean they are lost to you.