Post iudicium actrix iterum in scaena stat, et turba ei plaudit; laetitia in turba manet.

Post (when it means after) is a preposition that normally takes the accusative. So post iudicium uses iudicium = accusative singular of iudicium, -iī (judgment / trial / verdict).
(Compare: post + accusative is standard; unlike some prepositions, it doesn’t switch meaning by case.)

In second-declension neuter nouns, the nominative and accusative are identical in form (both singular end in -um). You identify the case from syntax: here it must be accusative because it’s the object of the preposition post.

Actrix is nominative singular feminine, meaning a female actor (actress). It’s the subject of stat.
The masculine equivalent would be actor (nom. sg.), not actorem—actorem would be accusative and wouldn’t fit as the subject here.

Latin often uses the present tense to narrate events vividly (sometimes called the historical present), especially in storytelling or lively description. So stat can describe a scene as if it’s happening right now, even if the broader context is past.

Iterum is an adverb meaning again. It modifies stat (the standing happens again).
Latin word order is flexible; placing iterum near actrix or near stat is common. The placement can slightly affect emphasis, but the basic meaning remains again.

In takes:

• ablative for location where (being/standing in a place) → in scaenā
• accusative for motion toward (going into a place) → in scaenam

Since stat is standing (no motion into), Latin uses in + ablative: in scaena.

Scaena is ablative singular here (because of in + ablative). It’s a first-declension noun: scaena, -ae.

Turba is nominative singular and is the subject of plaudit. Even though it refers to many people, it’s grammatically singular (a collective noun), so the verb is also singular: plaudit.

Ei is the dative singular of is, ea, id (here meaning to her).

• eam would be accusative (her as a direct object).
• eī is often written with a macron to show a long vowel, but many texts omit macrons; ei and eī are the same form.

In Latin, plaudere commonly takes a dative for the person being applauded/approved: plaudere alicui = applaud someone / applaud for someone.
So turba ei plaudit uses ei correctly as the indirect object.

The semicolon is just punctuation to separate two closely related statements. Latin manuscripts didn’t use modern punctuation consistently; editors add punctuation for readability. Grammatically, nothing special happens because of it.

Because laetitia is nominative singular, and manet agrees with it (3rd person singular). In turba is a prepositional phrase in the ablative describing where the happiness remains. So the structure is: [Subject] laetitia + [verb] manet + [where] in turba.