Q: Where is my user dictionary stored?
You can manually edit it in any text editor.
Q: Is there an ability to add custom dictionaries to ReSpeller, e.g. for other languages?
A: No, there isn't. May be it will be possible in next versions. But you can add some words into "user.dic"
Q: In VS2012 I have several menu items of ReSpeller after ReSpeller update
A: It's a strange bug of VS2012+ReSharper 7 bundle. Remove <Profile>\AppData\Roaming\Microsoft\VisualStudio\11.0 directory to fix it. All your settings of VS will not be deleted.