Can Linux run in background with Win at foreground
 

Hi,
I would like to use an application that heavily depends on Linux kernel and in the same time run Windows on the same machine. Something like Windows works foreground and Linux background... is it possible?

You would need a Virtual Machine (VM)--eg VMWare, Qemu, Xen, etc. Do some Googling using "virtualization", etc. to get your feet wet.

Would I be able to run that application at the same time while running Windows on the same machine?

VM software runs on the host OS--be it Linux or Windows. Then the guest OS runs on the virtual machine.
There are various combinations possible.

Unless you're willing to work pretty hard at it, I think your best bet might be an inexpensive commercial program called, Parallels. Google it.

Check out VirtualBox. I use it to emulate winxp to do testing of web development stuff on my debian host.