The definite articles in German are technically demonstrative pronouns/adjectives, so they serve a dual function. In “Klaus hat Hans getroffen. Der ist Arzt,” “der” is often used instead of “er” in colloquial language to refer to Johann instead of Peter (the person who was mentioned later rather than earlie).
Ja, "ich esse alle Kartoffeln" can also mean: I eat all kinds of potatoes. This meaning is clearly expressed in the follwing sentence: "Ob fest kochende oder mehlig kochende Kartoffeln, ob Frühkartoffeln oder Spätkartoffeln, ob Süßkartoffeln oder Kartoffeln aus der Region, ich esse alle Kartoffeln. "
Both "all the.." and "all of the.." are correct phrases in English. (One is perhaps more favored in some regions over the other, but personally, I use both, just depending on my mood!) There are other English amount phrases that can drop "of the" depending on the region/person: "a few (of the) potatoes" or "a couple (of) potatoes."
However, other amount words in English like "a lot," "some," "part," "none," need "OF the.." after to make sense. You can say, "I eat part of the potatoes," but NOT "I eat part the potatoes." Same with "none of the potatoes" - NOT "none the potatoes." "A lot" needs "of," but can drop "the" depending on if you're talking about specific or general nouns: "I am eating a lot of the potatoes that you cooked," or "I eat a lot of potatoes in my diet." Also, "some" is similar to "all," but a bit different too. You can say, "I eat some OF THE potatoes," or "I eat some potatoes," but NOT "I eat some the potatoes."
I hope I didn't just create more confusion! English is a truly insane language, and I'm constantly thankful it's my native one!
Hm, yes in a sense. It would mean that you are eating each and every one. So if you're emphasising for instance how good the potatoes are you could say "These potatoes are so good, I'll eat each and every one of them!" the meaning is the same as "I'm eating all of them" but it's a slightly different sentiment :)
Adjectives do have endings according to gender, number, and case.
Here, Kartoffeln is plural, though and gender is not distinguished in the plural -- so alle Äpfel (masculine plural), alle Kartoffeln (feminine plural) and alle Pferde (neuter plural) all have the same adjective ending.
Does “alle” decline like an adjective with no article?
I think so, yes.
Would it be -en, -e, -es, -e (for masculine, feminine, neuter, plural) in accusative?
In theory, yes.
In practice, alle is almost always used only in the plural.
I would prefer den ganzen / die ganze / das ganze ... in the singular.
"Ich alle Kartoffeln gegessen." would literally translate to "I eaten all the potatoes." Plus, in German, you always have to have a verb at the second position of a main sentence. If you wanted the word from the same origin as English "ate," that would be aß, but you wouldn't see "Ich aß alle Kartoffeln." except in a novel about a man who went on a quest to eat all the potatoes.