Yes there are quite a few that the stylus is completely optional.
Yes, it is possible to play most games using a finger instead of the stylus, however, the accuracy is very poor and many games require the precision that only the stylus can deliver.
With a Nintendo DS Stylus, one can play certain games better, the user input is more precise which leads to a better user experience. The stylus pen also makes it easier to touch smaller part of the screen that a finger might be too big to reach.
APPROX. 214g including battery pac and stylus.
Yes, the 2DS can play 3DS games since it is basically a 3DS but flat and without 3D.
On the Nintendo Wii, you can play obviously Wii games and Nintendo Gamecube games.
Yes and no. There are NDS games as well as NDSi games but both can be played on the Nintendo DSi and Nintendo DS
There are more that a thousand games for nds. You can even play Nintendo advance games on it.
You can probably get out of the house or play board games and also you can take or your nintendo DSI or nintendo 3DS or nintendo
yes
no
no
No.