I would like to confirm to you guys, if the above api reference is compatible with ArcGIS 9.3? And Is it ok to use Visual Studio 2008 for that ESRI API for WPF 2.2 version?
This page lists installation requirements (VS 2008 with .NET Framework 3.5 is supported): http://help.arcgis.com/en/webapi/wpf/help/index.html#//01n70000001v000000.htm. It should be compatible with ArcGIS Server 9.3.1 also but keep in mind that ArcGIS Server 10 functionalities exposed in the API will not work for you as you are limited by your server version.
