In a nutshell:
Q1: When do we not use an article in front of an adjective?
This depends on wether you want to talk about specific things or about some things. Also the usage of singular or plural has an influence, and there are also some words that can't have a plural form that behave different.
Q2: In the sentence, it is written that adjectives without an article take the ending of an article. But, if it has no article, which article's ending does it even take?
They don't take the ending of an existing article. They take the ending that an article would have if there was an article. What this sentence wants to say is this:
There is an ending that indicates the grammatical case. If there is an article, this ending sits at the end of the article. But if there is no article, then this ending sits at the end of an adjective.
In detail:
German has three kinds of articles:
definite articles
der, die, das, dem, den, des
Der kleine Ball fiel in den tiefen Brunnen, und die traurigen Kinder weinten.
You use this kind of articles if you are talking about specific (not any) things or persons. In English there is only one definite article: "the", and it is also used for specific things or persons.
indefinite articles
ein, eine, eines, einem, einen, einer
Ein kleiner Ball fiel in einen tiefen Brunnen.
You use this kind of articles if you are talking about some or any things or persons without meaning specific things or persons. In English there are two definite articles: "a" and "an", which are used the same way as the German indefinite articles.
The German indefinite articles are all homonymes of the numeral "ein" ("one" in English), so in German the translations of the Englisch nominal groups "one apple" and "an apple" are identical:
I had three apples. I ate two of them and now there is only one apple left.
Ich hatte drei Äpfel. Ich habe zwei davon gegessen und jetzt ist nur noch ein Apfel übrig.
What do you have in your bag? - That's an apple.
Was hast du in deiner Tasche? - Das ist ein Apfel.
This has two consequences:
- numerals influence adjective endings the same way as indefinite articles do in German. (I'll talk about this in a minute.)
- indefinite articles can only be used in the singular form in German. (This is true for English too.)
the null article
This is just a way to say, that there is no article at all, at a place where you normally would expect an article. I use the symbol ~ to display a null article, but in real sentences there is just nothing.
~ kleine Bälle fielen in ~ tiefe Brunnen, und ~ traurige Kinder weinten.
Kleine Bälle fielen in tiefe Brunnen, und traurige Kinder weinten.
Here I used the null article as an indefinite article for plural forms, which we also can do without adjectives:
~ Bälle fielen in ~ Brunnen, und ~ Kinder weinten.
Bälle fielen in Brunnen, und Kinder weinten.
But it's also used for singular forms, if the noun is a word of which there is no plural form, like names of materials, feelings and other things:
~ Wasser ist eine Flüssigkeit und ~ Luft ist ein Gasgemisch.
Wasser ist eine Flüssigkeit und Luft ist ein Gasgemisch.
~ Liebe und ~ Hunger sind zwei unterschiedliche Gefühle.
Liebe und Hunger sind zwei unterschiedliche Gefühle.
The null article is also an indefinite article in these usages, and it can also be combined with adjectives:
~ kaltes Wasser ist eine Flüssigkeit und ~ warme Luft ist ein Gasgemisch.
Kaltes Wasser ist eine Flüssigkeit und warme Luft ist ein Gasgemisch.
This three kinds of articles influence the way how adjectives are declined, that are used as attribute of the noun to which the article belongs:
definite article
If you use a definite article, then the article already indicates the grammatical case, and so the adjective doesn't need to do that too. So, the adjective is only weakly declined ("schwache Beugung"; "schwache Deklination") if there is a definite article.
Nom: Auf dem Tisch liegt das trockene Brot.
Gen: Martin bemächtigte sich des trockenen Brotes.
Dat: Dieser Stein ähnelt dem trockenen Brot.
Akk: Sandra sieht das trockene Brot.
null article
Having the null articles means in fact: There is no article. So, in this case there is no article that could show which case is used for the nominal group to which it belongs. So, it's the adjective's job to display this information, and therefore it must be declined strongly ("starke Beugung"; "starke Deklination")
Nom: Auf dem Tisch liegt trockenes Brot.
Gen: Martin bemächtigte sich trockenen Brotes.
Dat: Dieser Stein ähnelt trockenem Brot.
Akk: Sandra sieht trockenes Brot.
indefinite article
If there is an indefinite article, then the adjective is in some situations declined weakly and in other situations strongly. We call this behaviour "mixed declension" ("gemischte Beugung"; "gemischte Deklination")
Nom: Auf dem Tisch liegt ein trockenes Brot.
Gen: Martin bemächtigte sich eines trockenen Brotes.
Dat: Dieser Stein ähnelt einem trockenen Brot.
Akk: Sandra sieht ein trockenes Brot.
Words that are not articles, but behave like articles
I already said, that the numeral "ein" (in English: "one") behaves exactly identical as the article "ein" (in Englisch: "a" or "an"). But there are more words that behave like articles:
behaves like a definite article
diese, jede, welche, solche, alle
Use weak declension if the determiner of the nominal group is one of these words.
Examples:
Dieses trockene Brot möchte ich nicht essen.
Das gilt für jedes trockene Brot.
Welches trockene Brot meinst du?
Solche trockenen Brote möchte ich nicht essen.
Das gilt für alle trockenen Brote.
behaves like the null article
viele, manche, mehrere, einige
Use strong declension if the determiner of the nominal group is one of these words.
Examples:
Hier gibt es viele trockene Brote.
Manche trockene Brote werden nicht mehr gegessen werden.
Auf dem Tisch liegen mehrere trockene Brote.
Auf dem Tisch liegen einige trockene Brote.