Learn Hardcore German: Der Stapel Briefe ist genial sortiert: nach Datum, Absender und Filiale. - The pile of letters is brilliantly sorted: by date, sender, and branch.

Because the grammatical subject is singular: der Stapel (the pile). So the verb agrees with Stapel: Der Stapel … ist …. If you made the letters the subject, you’d say: Die Briefe sind genial sortiert …

Is Der Stapel Briefe correct, or should it be Der Stapel von Briefen?

Both are possible. The more idiomatic, concise phrasing with collective/measure nouns is without von: ein/der Stapel Briefe, eine Tasse Kaffee, ein Glas Wein. The von-variant (ein Stapel von Briefen) also exists and can sound a bit heavier or more colloquial/emphatic. A one-word alternative is the compound noun der Briefstapel (“letter pile”).

What case is Briefe in Der Stapel Briefe?

Effectively a genitive-like complement (often called a partitive/measure genitive). With plurals, the form looks the same as nominative/accusative plural. You can see the genitive behavior if you insert an adjective:

ein Stapel alter Briefe (genitive plural adjective ending -er).

Why are there no articles after nach (no dem/der)?

In classifying phrases, German often uses nach + bare noun to mean “by/according to [category]”: nach Datum, nach Größe, nach Farbe. Adding an article would point to a specific referent: nach dem Datum = “by the date (specific one).” Here we’re naming general sorting criteria, so no articles.

Which case do nouns take after nach?

Dative. With articles you’d get:

nach dem Datum (das Datum)
nach dem Absender (der Absender)
nach der Filiale (die Filiale) In the sentence, the articles are dropped because we’re listing general categories.

Why are Datum, Absender, Filiale in the singular and not plurals?

When you name sorting criteria, German usually uses the singular as a label: nach Datum/Größe/Farbe. Plurals are possible but less idiomatic here. Compare:

nach Absender (by sender, as a category)
less common: nach Absendern (by senders)

Does genial mean “friendly” like English genial?

No—false friend. German genial means “brilliant, ingenious, outstanding.” Here it’s an informal, positive intensifier: genial sortiert ≈ “brilliantly/excellently sorted.” If you just want neutral praise, gut sortiert works.

What exactly is ist … sortiert—some kind of passive?

Yes, it’s the “stative passive” (Zustandspassiv): ist sortiert describes the resulting state. If you emphasize the sorting action, use the event passive (Vorgangspassiv):

Die Briefe wurden genial sortiert … (they were sorted). Perfect active is also possible if you name the agent:
Jemand hat die Briefe genial sortiert …

Can I put the nach-phrase inside the clause instead of using a colon?

Yes: Der Stapel Briefe ist genial nach Datum, Absender und Filiale sortiert. Repeating nach is optional: … nach Datum, nach Absender und nach Filiale. The colon is just a stylistic way to introduce the explanation/list.

Should the word after the colon be capitalized?

Only if what follows is a full sentence or starts with a noun anyway. Here, nach remains lowercase, which is correct: … sortiert: nach Datum …

Do I need a comma before und in the list?

No. German does not use the Oxford comma in simple lists. So Datum, Absender und Filiale is correct (no comma before und).

Why Absender and not Sender?

der Absender = the sender of a letter/parcel (the person/address it comes from).
der Sender = transmitter/broadcaster/channel, or a sending device. For mail, Absender is the right word.

Could I say Briefstapel instead of Stapel Briefe?

Yes: Der Briefstapel ist genial sortiert: … It’s a standard compound and often sounds very natural. Meaning and grammar stay the same.

Why Briefe and not Briefen—shouldn’t plurals take -n in the dative?

The -n ending is for dative plural in contexts that require dative (e.g., mit den Briefen). After Stapel, we’re not in the dative; we’re using a bare (genitive-like) complement. Hence (ein) Stapel Briefe, not Briefen.