Instead of horizontal or vertical, can i build a menu like a square like so?
Yes you can create this custom menu with Wix.
First you would need to add a container/box around all the elements. Then add the vector images and text, select both and group them together. Then take the group and on click make it redirect to the appropriate page.
When that is all done you would need to set it as hide on load, and when a user clicks something (an event) this container would show.