How to "flatten" in Inkscape?

Question

I know that Inkscape has no flatten function. But. I have three objects in an svg file, which I want to all merge into one. It's a contribution to the Material Design Icon catalog, so this has to be a single path SVG.

However, when I "Union" the objects, two of the inner objects become thinner. If I "Combine" them, the outer object becomes fatter. Think it may have something to do with stroke and fill, but tinkering with these doesn't change anything.

Isn't there a function that just converts whatever is visible into one shape?

Juancho suggested doing "Stroke to Path", this works in the sense that the dimensions are now kept the same. But I fail to get the background (fill?) back on the outer ring afterwards:

This is the raw SVG:

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg
   xmlns:dc="http://purl.org/dc/elements/1.1/"
   xmlns:cc="http://creativecommons.org/ns#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
   xmlns:svg="http://www.w3.org/2000/svg"
   xmlns="http://www.w3.org/2000/svg"
   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
   version="1.1"
   width="24"
   height="24"
   viewBox="0 0 24 24"
   id="svg4"
   sodipodi:docname="pentagram-circle-outline.svg"
   inkscape:version="0.92.4 (5da689c313, 2019-01-14)">
  <metadata
     id="metadata10">
    <rdf:RDF>
      <cc:Work
         rdf:about="">
        <dc:format>image/svg+xml</dc:format>
        <dc:type
           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
        <dc:title />
      </cc:Work>
    </rdf:RDF>
  </metadata>
  <defs
     id="defs8" />
  <sodipodi:namedview
     pagecolor="#ffffff"
     bordercolor="#666666"
     borderopacity="1"
     objecttolerance="10"
     gridtolerance="10"
     guidetolerance="10"
     inkscape:pageopacity="0"
     inkscape:pageshadow="2"
     inkscape:window-width="1722"
     inkscape:window-height="999"
     id="namedview6"
     showgrid="false"
     inkscape:zoom="27.812867"
     inkscape:cx="12.701976"
     inkscape:cy="11.744741"
     inkscape:window-x="0"
     inkscape:window-y="0"
     inkscape:window-maximized="0"
     inkscape:current-layer="svg4" />
  <path
     d="M 12 2 C 6.47 2 2 6.5 2 12 A 10 10 0 0 0 12 22 A 10 10 0 0 0 22 12 A 10 10 0 0 0 12 2 z M 12 4 A 8 8 0 0 1 19.722656 9.9179688 A 7.5696538 7.4413764 5.2319768 0 1 19.722656 9.9199219 A 7.5696538 7.4413764 5.2319768 0 1 20.044922 11.904297 A 7.5696538 7.4413764 5.2319768 0 1 19.140625 15.587891 A 8 8 0 0 1 12 20 A 8 8 0 0 1 4 12 A 8 8 0 0 1 12 4 z "
     id="path2"
     style="fill:#000000;fill-opacity:1;stroke:#000000;stroke-opacity:1;stroke-width:0;stroke-miterlimit:4;stroke-dasharray:none" />
  <path
     inkscape:connector-curvature="0"
     style="display:inline;fill:#030000;fill-opacity:1;fill-rule:nonzero;stroke:#000000;stroke-width:0.40000001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
     d="M 12.091785,4.6840407 7.6392526,17.907485 12.129207,14.886198 16.54432,17.867474 Z m -0.03789,2.140559 3.126247,9.3421803 -3.107775,-2.180816 -3.1262453,2.180816 z"
     id="path4048"
     sodipodi:nodetypes="cccccccccc" />
  <path
     inkscape:connector-curvature="0"
     style="display:inline;fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:#000000;stroke-width:0.40000001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
     d="m 4.8751298,9.9191537 6.5719872,4.4869193 h 1.36418 l 6.33373,-4.4296539 z M 7.2977352,10.665597 H 16.96068 l -4.906786,3.380383 z"
     id="path3166"
     sodipodi:nodetypes="ccccccccc" />
</svg>

Answer 1

The paths have different stroke styles.

Therefore you must first get rid of strokes by turning them into paths as well.

Select everything, Path -> Stroke to path, then Path -> Combine.