Options for operating phone remotely For Remote Desktop functionality there is Droid VNC Server, other current better options?
Android Screencast (Seems like something that was promising)?

I used to "Wi-Fi keyboards", but now with VNC its not so interesting, as I have to set the input-method on the phone.  (i think "Remote Keyboard" app could be interesting if there are situations when VNC are difficult. 

What about options for working directly with the phone, like desktop SMS applications?

I am thinking of any way of connecting (Bluetooth, USB, Wi-Fi....) with a rooted phone?

Primarily Windows Desktop (But many possibilities is always better)
You can hae a look at AirDroid for desktop SMS.

It works as a kind of web server on your phone, which means you have to access it from a secure web page (downside: works only inside the same WiFi network).

But next to smses you can do a lot more with it, but I recommend you have a look at it yourself.