For widgets that support text content, like an Image widget, you can select the widget(s) in in the editor, then look at the bottom of the STYLE panel to view the padding amounts. This shows the internal padding used for text layout.
Yes, if you change any of the padding values the result will be shown immediately in the editor, and upon a refresh/republish, it will be shown in the browser.
No, there is nothing in Axure that directly supports dynamic access to padding values for widgets; either reading or setting values. I suppose you could build something manually in which you create a dynamic panel with multiple states–one for each padding amount you need. You’d have to manually create the padding differences in the editor and then wire in the dropdown to change the dynamic panel (dp) to the correct state to show the padding difference. For efficiency, especially if you have large image(s) or a lot of different padding settings, I’d recommend separating the text and image, placing the text content in the dp states–with the default null fill for the dp. Size this dp with same dimensions and x,y location as your image and place in front of the image. Otherwise, you could just place your image with text content, set the default padding amount, then right-click it, select “Create Dynamic Panel”, double-click to access State1, duplicate State1, change the padding for the image in that state, duplicate State2, set padding, etc.