The filled open bezier issue (problem 4) probably needs a fix something along these lines:
1. Draw a second bezier curve identical to the first except that it is closed and the stroke is not visible.
2. Fill the second bezier curve with the fill properties from the original Inkscape SVG object.
3. Draw the primary bezier curve over it. Do not close this Bezier, do not fill it.
The filled open bezier issue (problem 4) probably needs a fix something along these lines:
1. Draw a second bezier curve identical to the first except that it is closed and the stroke is not visible.
2. Fill the second bezier curve with the fill properties from the original Inkscape SVG object.
3. Draw the primary bezier curve over it. Do not close this Bezier, do not fill it.