Is there a way to open new child windows or switch between open child windows in the WinBox GUI?
What are the WinBox hotkeys and keyboard combinations that manage child windows?
Are there any keyboard shortcuts that I can use with the WinBox GUI?

List of keys that I know.
Control-C – keyboard interrupt.
Control-D – log out (if input line is empty)
Control-K – clear from cursor to the end of line
Control-X – toggle safe mode
Control-V – toggle hotlock mode mode
F6 – toggle cellar
F1 or ? – show context sensitive help. If the previous character is \, then inserts literal ?.
Tab – perform line completion. When pressed second time, show possible completions.
Delete – remove character at cursor
Control-H – remove character before cursor and move cursor back one position.
Control-\ – split line at cursor. Insert newline at cursor position. Display second of the two resulting lines.
Control-B – move cursor backwards one character
Control-F – move cursor forward one character
Control-P – go to previous line. If this is the first line of input then recall previous input from history.
Control-N – go to next line. If this is the last line of input then recall next input from history.
Control-A – move cursor to the beginning of the line. If cursor is already at the beginning of the line, then go to the beginning of the first line of current input.
Control-E – move cursor to the end of line. If cursor is already at the end of line, then move it to the end of the last line of current input.
Control-L – reset terminal and repaint screen.

Almost all of those are for the CLI.
There must be more hotkeys for the GUI than F6 (child window focus switch)?

Shift + F6 only reverses the window switching order.