Just an addition to druban's advice. As new Inkscape user, things may look a bit overwhelming.
The problem with your fills is that you currently have open paths. There are 2 steps required to make a single object from separate paths:
1. Combine the paths (CTRL+K or Path > Combine from the menu). Now you have many subpaths, and the object cannot be filled as the path is open.
2. Join the open nodes. Use the Node Tool, select the endnodes that must be joined and join them ("join selected end-nodes" - 3rd icon on the Node Tool - Control Bar).
After this step you can fill the whole part with the desired colour.
Tho the subject is something entirely different - these steps are explained in the first minute of my
flora design video tutorial.
Note that you have Path Tools available that allow you to easily knock out parts (for example: place the circle in the centre on top of your fully filled 1st shape, then select both objects and use Path > Difference (this will subtract the top object from the bottom).
And another note - if combining all the subpaths seems a bit too much work:
- Inkscape has a cool gear generation option: Extensions > Render > Gear
- You could import the shape as a bitmap (or Edit > Make a bitmap copy) and then trace your own shape (Path > Trace Bitmap).
I hope this gives you enough information to recreate your work.
Cheers,
Syllie