That list shows the fill available in the current map. If you want fills from another style you need to import them into the map first, then they will be available to pick from that dialog.

None of the tools do that automatically as far as I know. You'll need to manually place each node. Turn on Snap and it should be real easy to place the nodes precisely.

This isn't a symbol, it is a drawing tool. The "thing" in the symbol catalog is a fake symbol to allow drawing tools to be show in the symbol catalog.

You'll need to edit the drawing tool itself, but note that the fill used by this tool is a hatch style, which is a fill defined in a separate drawing found in @Hatch Styles

The PPI setting is a meaningless value outside of print calculation. Just completely ignore it and always just concentrate on the width/height in pixels.

The important thing to check is that both height and width is set correctly, since CC3+ will crop the value if necessary to retain the ratio. (Well, technically, all you have to do is to get one correct, and just set the other one to a really high value, since it will be capped at the max allowed by the aspect as long as the rectangular section is specified correctly.)

When doing the rectangular export, for perfect precision, I recommend turning on cursor snap so you don't have to align them perfectly manually.

To make sure the export is done correctly from CC3+, you should be able to check that the pixel dimensions are correct from the file properties in Windows (or by opening it in an image editor)

Should be a border tool available among the various drawing tools. Click :CC2DRAWTOOLS: to see them all.