a) override paintWidget() and carefully put your rendering code in there - best to use LWJGLRenderer.pauseRendering() and resumeRendering(). You will need to setup the view port based on the position & size of the widget. You can take a look at the TWL Theme Editor - it does this to render the preview in the bottom center.
b) a button will set the "hover" animation state while the mouse is over it
a) Could you plese clarify the anwser? How can overriding a paintWidget method with the rendering code put the view port into the resizable frame? I dont even think that method is somehow related to the ResizableFrame class.
b) I wanted to ask how can i check if the mouse is over the button!
Please write no more anwsers like "bananas are yellow" when i ask you "how can i change the color of bannanas"... I'm not trying to make you feel bad, i'm just really pissed, because the documentation of TWL is awful, just like your anwser.