Is there a way to do this so it doesn't open a new window when it switches to that desktop? IE if Outlook is assigned to Desktop 1 and is currently open, and I click on the outlook icon when I'm in Desktop 2, it moves to desktop 1 but opens a new Outlook window. Instead, can it just move to the existing Outlook window that's already open?

Check out the "Desktop Rules". Use the assistant. The conditions for the applications you mentioned as examples should be in the rules database. Add a "Move" action for the desktop you want to assign the application to.

Let us know if you need any further help with this.

Is there any way to assign a specific application to a space. In other words, if you have 4 spaces, can you assign Outlook to always open in space 1 and Firefox in Space 2 etc?
Thanks.