How can I play an online video in full screen AND type in a text editor at the same time?

Unfortunately I don't think there is a way to do this. Despite the addition of things like AreoSnap in Win7; windows still doesn't handle handle dual monitors well in all instances. Full screen applications only working when they've got system focus is the most painful example. IIRC the latest version of WMP on Win7 does what you want it to do; but as a sole exception to the default behavior I suspect it's a case of the WMP team bludgeoning their way around an OS limitation vs a native way to get proper behavior being added.

Without support from the Windows Team I suspect the best we'll be able to get anytime soon would be for the plugin/browser makers to create a "maximize video to tab" feature that would play in the entirety of the tabs space, while hiding the menu/status/address bars to get a pseudo-full screen effect while still running as a normal mode application.

Use "Dexpot" (Windows 7). This is similar to Ubuntu's multiple Workspace.

http://www.dexpot.de/