Is it possible to have ASP site with MS Access database hosted on Linux or is it possible to convert MS Access to some other format to do so?

Welcome to WHT :)

From MS Access you can export to CSV and then import into any database.

There are also MS Access readers available for Linux (but I doubt any hosting company will let you run that on their servers).

You can have an ASP site hosted on Linux, but it requires a special extension that is not free, so unless your site is very large, or you are willing to pay for the extension, not many hosts will be accomodating.

Like fyrestrtr has said, it is possible with some extra works. I would suggest that you keep it simple and host those type of framework applications on a Windows hosted system, if you are OK with Windows Hosting providers. If not, then it would be wise just to import your data into a MySQL database, code the framework in PHP and house it on a Linux hosting server.

With regards to running ASP on linux, Cobalt RaQ's do it out the box :) (using chillisoft asp)