You can define

 para = Sequence[BoundaryStyle -> Thick, AxesEdge -> {{-1, -1}, {-1, -1}, {-1, -1}}, Boxed -> False]

then use

 ParametricPlot3D[{u, v, 0}, {u, 0, 1}, {v, 0, 1}, Evaluate[para]]

----

Explanation:

`Sequence` will automatically expand inside of an expression.

 In[]:= {1, Sequence[2,3]}
 Out[]= {1, 2, 3}

`Graphics` does accept options given as a list (`Graphics[{Circle[]}, {Axes -> False, Frame -> True}]`), but many other functions won't. So we need to use `Sequence`.

`BoundaryStyle` is an option for `ParametricPlot3D`, but not for `Graphics`, therefore it can't be given in `Show`. So we have to pass the options to `ParametricPlot3D` directly.

`ParametricPlot3D` has the `HoldAll` attribute, which means that `para` needed to be wrapped in `Evaluate` to make sure that `ParametricPlot3D` will see the actual options and not the symbol `para`.