Can the windows be set to minimize to a dock? For example, Im using GNOME shell with unity 2D and I would prefer the windows to minimize to their respective launcher. Example: instead of the open window minimizing to its icon in the launcher, it goes to the corner.
I recommend not minimizing your windows. The minimize and maximize buttons have been removed from windows in Gnome Shell for a reason. There's really no need to minimize windows, so if you're going to use Gnome Shell, I would recommend kicking the habit. Gnome Shell has an amazing way of handling workspaces, I recommend using it. I don't see a workspace switcher launcher on your Unity bar in your screenshot, so I'm taking Gnome Shell handles your workspaces? Either way, with workspaces you never have to minimize windows. The advantage of having Unity is that you could quickly go to that application on whichever workspace by clicking on its launcher.
Interesting setup you have there, like Uri Herrera already mentioned.
As far as i know what you are asking is not possible, since the unity launcher dock to the left prevents you from having a dock at the bottom of your desktop in a gnome-shell environment, since you have this special setup of choice.
The best way to go about it, is to use a workspace shell-extension, in combination with an application window switcher (and maybe an index launcher application, like gnome-do or synapse)
There are many more variations and alternatives, in form of shell-extensions, regarding the handling of workspaces and applications/windows here.