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

Win98 or higher works.
http://msdn.microsoft.com/downloads/default.asp?url=/downloads/sample.asp?url=/msdn-files/027/001/829/msdncompositedoc.xml

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

Here are some resources to help you make your decision:
http://msdn.microsoft.com/vbasic/techinfo/articles/upgrade/guide.asp
http://msdn.microsoft.com/library/default.asp?url=/library/en-us/dnvb600/html/vb6tovbdotnet.asp
http://www.aivosto.com/vbtips/vbnetmigration.html
http://www.devx.com/upload/free/features/vbpj/2000/12dec00/bh0012/bh0012.asp