Post cenam mater in horto orat et pacem sperat.

In Latin, post is a preposition that normally governs the accusative when it means after (in time) or behind (in space). So post cenam literally means after the dinner/meal.

• cena = dinner (feminine noun)
• cenam = accusative singular, required by post

Yes. cena refers to the meal itself, so post cenam means after dinner (the meal)—i.e., once dinner is done.

mater is nominative singular, and it’s the subject of the verbs orat and sperat. Many Latin nominative singular forms don’t end in a very obvious “subject marker.”
mater belongs to the 3rd declension and has an irregular-looking nominative form (compare genitive matris).

With in, Latin uses:

• ablative for location (in / on / within)
• accusative for motion into (into / onto)

So in horto (ablative) means in the garden (staying there), not into the garden (movement).

• hortus = garden
• horto = ablative singular

You would use the accusative: in hortum.
So: mater in hortum... would imply she goes into the garden.

Both are present tense, 3rd person singular:

• orat = (she) prays / is praying
• sperat = (she) hopes / is hoping

Latin present tense can often cover both English simple present and present continuous depending on context.

Because the verb endings carry the person/number information. -t marks he/she/it (3rd singular). So orat already includes she/he/it prays. The subject mater makes it clear it’s she.

orare can mean to pray, to beg, or to plead, depending on context. In a sentence like this, especially paired with pacem sperat (hopes for peace), orat is most naturally understood as prays.

Because sperat (hopes) is a transitive verb that takes a direct object in the accusative. So pacem is what she hopes for: peace.

• pax (peace) has accusative singular pacem.

Not usually with sperare. Standard Latin uses sperare + accusative for what is hoped for: pacem sperat. Using a preposition would typically change the structure and often sound non-idiomatic for this meaning.

Latin word order is flexible because endings show grammatical roles. Your alternative is grammatically fine. The original order Post cenam... foregrounds the time (after dinner) first, which is a common storytelling choice. Changes in word order often shift emphasis rather than meaning.

et joins the two verbs: orat et sperat = prays and hopes. Since both verbs share the same subject (mater) and the same time/location phrases, Latin doesn’t repeat those elements.

Yes. By default, a shared phrase like in horto is understood with both verbs unless context suggests otherwise. So she prays in the garden and hopes for peace (while) in the garden.

It functions as a prepositional phrase that gives time (an adverbial idea). In English we’d call it an adverbial phrase: it tells when the actions happen.