Ok, I think I am starting to understand.
Zorin Core uses Gnome Desktop. Zorin Lite uses XFCE4 desktop.
You installed the XFCE4-panel on the Gnome desktop, which most likely still had the Gnome-Shell running with its own panel.
When you add a new XFCE4 Panel, it is essentially a Blank. It is just as you describe, a small box placed on the desktop. In order to configure it, you must move it to the location you want it to be in. For example, the side, top or bottom (On bottom is the Gnome Panel, though).
Right click that box to open the XFCE4 panel settings. You can select its size; Length and Height. There are many settings available in the xfce4-panel settings window that opens. Unlike the gnome-panel, XFCE4 panel is highly configurable on Right Click.
If it is running the XFCE4-panel and you want it gone, you can run
killall xfce4-panel
This error means that an installation is in progress and you cannot get a lock on dpkg while it is currently locked by the running installation.
All of the above said… You were running the XFCE4 panel on the Gnome Desktop instead of XFCE desktop. While XFCE4 panel can run as a standalone package, which you did get it to do, it would be running in addition to the Gnome Shell with its panel and many dependencies for the xfce4-panel would not be present. This means that XFCE4-plugin packages, such as the equake package, would be not work.
I am speculating that you installed the panel in order to have access to the equake plugin?