Where is the correct place to store my application specific data?

Application properties - Most application data you described should be specific to each user and put in Environment.SpecialFolder.ApplicationData (the %appdata% environment variable). I would generally avoid putting data in the registry as it is hard to find, edit, and fix. If you do not want data to be associated with the user when they are roaming (maybe the files are big or connected to the computer in someway) then you can put it in Environement.SpecialFolder.LocalApplicationData (the `%localappdata% environment variable).

Global application data - I would put global application data in Environment.SpecialFolder.CommonApplicationData ( the %programdata% environment variable)

User specific application data - Same as #1, except when the data is intended to be easily found by the user (e.g. saved games) in which case it should go in Environment.SpecialFolder.MyDocuments, which has no associated environment variable.

As yas4891 points out you can reliably get these folder paths using Environment.GetFolderPath() using one of the Environment.SpecialFolder` values listed here.

Question 2:
I suggest using a subfolder in Environment.SpecialFolder.CommonAppData (maps to C:\ProgramData on Windows7 by default). This is a hidden folder.

Question 3:
Put those files into Environment.SpecialFolder.AppData(maps to C:\Users\[USERNAME]\AppData\Roaming by default, hidden folder), if you expect that the user does not intend to backup / modify those. Some games also put their save games into Environment.SpecialFolder.MyDocuments, probably because it is easier for users to find them there.

Example code:

var directory = Environment.GetFolderPath(Environment.SpecialFolder.AppData);


using (FileStream fs = File.Create(Path.Combine(directory, "myAppDirectory", "myFile.txt")))
{
    // write data               
}

For a complete list of special folders on Windows follow the link

SIDENOTES

• Users are allowed to move around those directories, so make sure you use the code provided above
• There is a bug in Windows 7 x64 regarding CommonAppData directory and the bug gets more severe in Windows 8 x64 CP. I've blogged about this: problems after moving CommonAppData directory on Windows 7 x64 and Windows 8 x64