I'll just do part ii) since you can already do part i)
If you start with the original parabola $${{\mathtt{x}}}^{{\mathtt{2}}} = {\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{ay}}$$
$$(2ap,ap^2)$$ This has a focal length of $$a$$ and a directrix of $${\mathtt{y}} = {\mathtt{\,-\,}}{\mathtt{a}}$$
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If you reflect this about the x axis it will turn upside down and you will have a parabola with a focal length of $${\left|{\mathtt{\,-\,}}{\mathtt{a}}\right|} = {\mathtt{a}}$$ and a directrix of $${\mathtt{y}} = {\mathtt{a}}$$ and the equation will be
The equation will be $$x^2=4(-a)y\;\;\rightarrow \;\;
x^2=-4ay$$
The parametric equation will be $$(2ap,-ap^2)$$
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If this is now translated down 2a units
The directix will translate down 2a units to $$y=a-2a\quad\rightarrow\quad y=-a$$
The focal length will still be $$a$$
The equation will be $$x^2=-4a(y+2a)$$
The parametric equation will be $$(2ap,-ap^2-2a)$$
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Therefore $$G(2ap,-ap^2-2a)$$
has the same focal length and directrix as the original parabola.
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Here is a graph to show what is happening
https://www.desmos.com/calculator/x2iznxi7bo