The Maple kernel (computational engine) is written in C, and the Maple Standard GUI is written in Java. The kernel and Std GUI run as separate processes, communicate with each over sockets, and mostly exchange representations of Maple's data structures (DAGs) in the same "dotm" (.m) format that is used to store expressions in its .mla library archive.
The kernel can do an external-call to run user-defined Java code. And the Java OpenMaple API provides mechanisms to run Maple code in the kernel.
But AFAIK there is no mechanism by which the Std GUI alone can do either of those things. No way to force the Java GUI to utilize some method (for something). OpenMaple talks to the kernel, not the Java GUI.
You could use OpenMaple to get the kernel to turn Maple language code into a Maple structure DAG which represents a Maple PLOT. But there's no function in the Java GUI for plotting it to any canvas, that which is available to OpenMaple, AFAIK.
If I properly understand the goals behind your 3 points, then I suspect that all are wrong in the ways that matter.