For a developer with a Java background, I am interested in exploring software development using the ASP.NET tools/platform as well.
Java web applications (.jsp and servlets) can run on many server platforms.
Question: Will a .NET web application be able to run in a Linux based server? Considering the scenario of not being able to use a Windows server for hosting a web app.
You can use Mono to run ASP.NET applications on Apache/Linux, however it has a limited subset of what you can do under Windows. As for "they" saying Windows is more vulnerable to attack - it's not true. IIS has had less security problems over the last couple of years that Apache, but in either case it's all down to the administration of the boxes - both OSes can be easily secured. These days the attack points are not the OS or web server software, but the applications themselves.