Conceptually you're asking a similar question to this, and some of your answers will be there. Perhaps read it first, then come back to the more specific answer at the bottom of my tirade here...
Illustrator (and most design software) does not work how you'd imagine it would or could. This is because it's all old.
It is all based on long forsaken programming paradigms for onscreen drawing that were themselves based on even older hardware technologies of computing that predate Windows and were trying to solve problems that weren't yet solved any other way.
So you have to come to terms with how these programs "view" screen based illustration before you can see how to solve problems like this with their VERY limited drawing tools.
You could argue that the mouse was never intended to be used for onscreen drawing, as the same guy that invented it had already spent much time working with onscreen digitisers/pens and saw them having different roles.
He envisaged the mouse as a selection tool in conjunction with a contextual interface for the left hand that further empowered the mouse's operability and functionality. Mostly this was all to do with textual editing, list making, etc. What we now consider "Office" software was the intended purpose of this interface, most certainly not illustration as the interface for that had already been solved - a digital pen.
But computing took a trip through the dark ages the moment the mouse was adopted because it was seen as a "one thing does it all" device and we never got the promised pen computing interfaces so sorely needed for creativity because Microsoft managed to successfully "enterprise" the entire world around doing the utterly mundane with computers and that being their prime directive.
As a result all the use paradigms of drawing software are complete rubbish and relate neither to artists nor to the potential of pen based input that's finally more frequently accessible.
If you're not yet committed to Adobe's Illustrator, I'd suggest backing away from it. It's not great. It's not even good.
You'll get this same thing done far faster, with much less agony, on an iPad with one of the drawing programs there. Oddly, most all of them suffer from being Adobe Illustrator clones. But at least they make a little more sense with direct manipulation than a mouse does for this kind of thing.
In Illustrator you have to think in terms of outlines and shapes.
A shape is nothing more than a closed outline.
So for this you need to complete the closed outlines into shapes, and then fill them with Black to get the desired outcome.
However nothing about working with outlines for drawing is fun.
If you can get an iPad it'll be far more enjoyable to use that.