There are no 'hidden charges' on the DSi.
You can buy some games from the Nintendo DSi Shop, which cost money, but that's optional.
Maybe not.
Sorry, there is no apps of any kind for the Nintendo Dsi. Maybe you could write to Nintendo to change that, though.
The DSi and Dsi XL do not have support for watching movies in any form.
No. The DSi not compatible with any Internet voice chat applications.
Yes , any game made for the DS will be compatible with the DSi and DSi XL consoles
No you cannot get Minecraft on a DSI XL. In fact you cannot get Minecraft on any Nintendo console.
DSi Ware games and other downloadable content The Nintendo DSi Shop is specific to the region for which the system was manufactured. For example, a Japanese system can download DSi Ware games and other software only from the Nintendo DSi Shop for the Japanese region, regardless of where the system is being played. Nintendo DSi exclusive game cards Nintendo DSi game cards that are only compatible with Nintendo DSi and Nintendo DSi XL (and not Nintendo DS or Nintendo DS Lite) are region locked. This means game cards manufactured for the U.S. market would not work in a system made for another country. Nintendo DS / Nintendo DS Lite game cards Older Nintendo DS and DS Lite software is region-free, so you can play most of that software on a Nintendo DSi and Nintendo DSi XL from any region. It's possible, however, that future Nintendo DS software will incorporate region encoding. In these instances, these games would not work in a system made for another country. Source: http://www.nintendo.com/consumer/systems/dsi/en_na/faq.jsp#vers
The Nintendo DSi is just an upgraded version of the Nintendo DS and DS Lite. The Nintendo DSi plays the exact same games as the Nintendo DS and DS Lite and only plays DS and DS Lite games. Currently, there aren't going to be any DSi games, only more DS games.
at any good gaming shop
You do not have to pay any money, above and beyond whatever you pay for your wireless internet connection, or any DSi points for use in the DSi store.
It's only on DSi, and possibly DSi XL, but I'm sure the iPhone or any smart phones have something similar.
No. Professor Layton and the Mask of Miracle is a game for the Nintendo 3DS and cannot be played on any version of the DS or DSi.