When I fill in the shape, it tends to not cover the whole shape from angle to angle, and it leaves gaps. When I try to fill again those gaps, it leaves again a small gap. How could I resolve this problem?

I'd use the bucket tool controls (top of window when tool is selected) to expand the fill, then send it behind the lines.

http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Bucket.html

http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Z-Order.html

This might be a case for the Shape Builder tool. 

Select your outline paths.
Duplicate [ctrl+d].
Activate the Shape Builder [x].
[click] the areas you want to fill.
[enter] to finish.
Set the fill colour.