>1. The developed applications using .Net, does it work on Windows 95/98 OS or not?

Applications written using Visual Studio .Net runs on Windows 98 but not 95. Visual Studio .Net itself does not run on Windows 98.

>2. If an application developed using VB6, can it be converted to .Net or it must be re-coded again ?

You better rewrite because the converter will not upgrade components to those of .Net (the grid for example). Wrappers will be used and then you will not be 100% .Net code (you will need to deploy those OCX).