Linux cross development?

I'm new to linux but have been running WinCE for a while.

Under WinCE and visual studio 2008, I can write and simulate/debug my
application on my Windows 7 machine.

Can I write / simulate code for embedded linux in the same way or do I need
to install the compiler/gcc on the Arm device and compile it on the device
only?

Where is a link for a simulator like Visual Studio provides?

Thanks.

You cross-compile on the host.

I believe QEMU is what you are after for a simulator.

I'd suggest having a look around buserror's site.
http://code.google.com/p/mini2440/

Then read this tutorial:
http://narnia.cs.ttu.edu/drupal/node/131

KernelKoncepts has some useful info as well.

Good luck!