
die Akte
file
A collection of documents and written materials about a specific case, person, or topic, usually kept in a folder.
Der Anwalt hat die Akte des neuen Mandanten sorgfältig studiert.
The lawyer carefully studied the new client's file.
file / act
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file
A collection of documents and written materials about a specific case, person, or topic, usually kept in a folder.
Der Anwalt hat die Akte des neuen Mandanten sorgfältig studiert.
The lawyer carefully studied the new client's file.

act
One of the main sections of a play or an opera.
Die dramatische Wendung ereignet sich erst im dritten Akt.
The dramatic twist does not happen until the third act.

to file away
To consider a matter settled and not deal with it any further.
Nach der Entschuldigung können wir den Streit zu den Akten legen.
After the apology, we can file the argument away.
In connection with documents, 'Akte' (file) is often combined with certain verbs. You can say 'eine Akte anlegen' (to create a file), 'eine Akte schließen' (to close a file), or 'Einsicht in eine Akte nehmen' (to inspect/read a file).
Die Polizei hat für den Fall eine neue Akte angelegt.
The police opened a new file for the case.
The word 'Akte' (file) is often part of compound nouns that describe the contents more precisely. Common examples are 'Personalakte' (personnel file, about an employee), 'Krankenakte' (medical file, about a patient), or 'Polizeiakte' (police file, about a criminal case).
Alle wichtigen Informationen über den Patienten stehen in seiner Krankenakte.
All important information about the patient is in his medical file.
The idiom 'etwas zu den Akten legen' (to file something away) is a fixed unit. The 'etwas' is replaced by the matter you consider settled. The form 'zu den Akten' remains unchanged.
Wir haben uns geeinigt, also können wir den Streit zu den Akten legen.
We have reached an agreement, so we can file the argument away.
act / nude / hassle
In a bureaucratic context, both die Akte and der Akt can be connected with a difficult matter. Die Akte refers to the collected documents, while der Akt colloquially refers to the laborious or complicated matter itself. When you mean documents, use “Akte”; when you mean the effort involved, “Akt” is more appropriate.

Die Sachbearbeiterin legte die Akte mit allen Unterlagen auf den Tisch.
The caseworker placed the file containing all the documents on the table.
Die Genehmigung für den Umbau war ein komplizierter Akt.
Getting approval for the renovation was a complicated hassle.