yes they are fully compatible (also with the dsi) (i've played together with a lite and a normal ds)
There is no such thing as "DSi Lite" but let me tell you this: at the moment of writing, ALL DS games fit in ALL DS's (DS, DS Lite, DSi, DSi XL)
The DS lite and DSi are completely different pieces of hardware. You would have to buy a DSi, you can not turn a DS lite into a DSi
Yes you can. You can also connect DSi to DS and DS Lite to DSi.
They are for ALL DS SYSTEMS, DS, DS lite, DSi, and DSi XL.
No. The DS range goes 'DS', 'DS lite', 'DSi', 'DSi XL', and then there 3DS.
Yes you can. You can also connect DS lite to DS and DS Lite to DSi.
Yes you can trade a DSi for a DS Lite at Gamestop.
No, the DSi uses a different charge to the DS lite.
No. The DSi and DSi XL does.
It is a DSi-enhanced game, meaning it works fine on DS and DS lite, and has additional features (WPA encryption and video chat) on DSi, XL and 3DS.
Yes, the Nintendo DS lite can play DSi games