The course has not covered every piece of Spanish content, and it was never going to. What it has done is take from every area of the language analytically, so that you can work out the rest yourself when you meet it.
The first puzzle. It changes in some places and not others.
Demasiados coches · Demasiado agresivo · Demasiado agresivos
So the answer comes from identifying what type of word follows, which the course has trained you to do all along. Demasiado is too, as in too many.
The word is long, but it breaks up: de más, "of more", plus -iado. And de más works on its own too: tengo cuatro de más is I have four too many, four spare.
The second puzzle. Ala, agua and aula are feminine words, yet they take el.
It is not simply that they begin with a: la alfombra and la almohada do too. The rule is narrower: two syllables, beginning and ending in a.
You can prove they are still feminine: el agua fría, not "frío".
The third puzzle. These lose their final o when a noun follows.
And it does not happen in the feminine: una mujer, alguna mujer, ninguna mujer.
No quiero ninguno · Quiero algún coche · No quiero ningún coche
All three puzzles turned on the same skill. Identifying what type of word you are looking at is mostly all you need to figure out what is going on.
Noun or adjective? Following a noun or standing alone? Feminine or masculine?
The point of the exercise, stated plainly: analyse what you come across, pick out what you do not understand, and tackle it so that you control it rather than the other way round.
And this is achieved not through memorising what is correct, but through analysing and understanding what is correct, and finding why.