Returning properties of plot

AbsoluteOptions for the first part of question.

Default styles for Axes, Ticks, Frame (DefaultAxesStyle, DefaultTickStyle, etc.) are options for GraphicsBox:

defaultstyles = Symbol /@ Names["Default*Style"]

graphicsDefaultStyles = DeleteCases[Quiet @ Options[GraphicsBox, defaultstyles], 
  HoldPattern[DefaultBaseStyle -> _]]

These styles are defined in style sheets and can be discovered using CurrentValue[{StyleDefinitions, stylename}]:

{#, CurrentValue[{StyleDefinitions, #2}]} & @@@ graphicsDefaultStyles // Grid

We can also use CurrentValue[{GraphicsBoxOptions, ...}] to get the default styles:

CurrentValue[{GraphicsBoxOptions, #}] & /@ defaultstyles