Inkscape requires the xlink: namespace for the href attribute on the <image>-tag.
Most browsers nowadays understand it without that, but it seems like Inkscape still requires it.
Simply change it to xlink:href= on the image element and add the xmlns:xlink="http://www.w3.org/1999/xlink" namespace to the <svg>-tag.
You could use Inkscape which is free, or virtually any vector image editor.
Copy and paste your signature image into Inkscape, lock it in place. Then draw the signature paths on top using the Bézier Tool (aka Pen Tool). Once you have finished unlock and delete the image.
You could use the Edit Paths by Nodes tool N to grab a path and bend it. There's no need to add any extra nodes to the rectangle for this to work.
What this really does is pulls out Bézier curves from the nodes.
When you have the rectangle selected using the Nodes tool N, click and drag a rectangle selection around all four nodes, this will select ...
This probably isn't relevant to this particular case, but for anyone looking here for answers it might be worth considering an experience I had -
One of my colleagues was dealing with another company and struggling to find a file format that worked for both of them. I said, how about asking them what software they're using. Guess what - it was Corel - same ...
In your SVG there seem to be several failed attempts to paint over the orange D with various strokes. You should delete these.
Instead, it would be better to use the Pen Tool to draw a rectangular patch, remove the stroke, fill it with the same green as the P, then bend the paths using the Bend tool so the patch fits over the D.
Note: to be able to do it ...
By experimentation, I was able to find the culprit: improper control characters. I used this tool: https://www.soscisurvey.de/tools/view-chars.php and found the 0x03 or ctrl+C where a cr lf characters ought to have been. The solution is very simple- from Adobe, backspace over the incorrect invisible 0x03 white-space and then hit return to replace it with the ...
It looks like you want to simulate an "elliptical brush".
To do that first create a circle with the circle-tool. The size doesn't matter as it will be just a "preview" of your brush. Just make sure it is not yet an ellipse, so hold the Ctrl-key while drawing it:
Next group that circle by itself (Ctrl-G) then scale and rotate the group ...