Post longum iter quies omnibus grata est.

Because post is a preposition that takes the accusative case when it means after.

So in:

• post longum iter

the phrase longum iter is in the accusative because it is the object of post.

A learner can think of it as:

• post
  • accusative = after ...

Other examples:

• post cenam = after dinner
• post bellum = after the war

Because this sentence says after a long journey, not during/by/with a long journey.

The noun iter is being governed by post, so it must be in the accusative singular:

• nominative: iter
• accusative: iter
• adjective agreeing with it: longum

This can feel strange because iter is a neuter noun of the third declension, and its accusative singular looks the same as the nominative singular:

• iter = nominative singular
• iter = accusative singular

But the adjective shows the case more clearly:

• longum = accusative singular neuter

So longum iter is definitely accusative.

Quies is nominative singular, and it is the subject of est.

We know this because:

• quies is the thing being described
• grata agrees with quies
• est is singular

So the structure is basically:

• quies ... grata est = rest is welcome / pleasant

Even though the word order is different from English, Latin often places the subject later or earlier for emphasis without changing the grammar.

Because gratus, -a, -um often takes the dative of the person to whom something is pleasing, welcome, or grateful.

So:

• omnibus grata est = is pleasing/welcome to everyone

This is a very common Latin pattern:

• mihi gratus est = he is pleasing/welcome to me
• nobis grata est = it is welcome to us

A good way to remember it is that Latin often uses the dative where English uses to:

• pleasing to everyone
• welcome to everyone

Because grata agrees with quies, and quies is a feminine singular noun.

Agreement in Latin means the adjective must match the noun in:

• gender
• number
• case

So:

• quies = feminine singular nominative
• therefore grata = feminine singular nominative

If the subject were a neuter noun, you would expect gratum instead.

Yes, quies is feminine.

Latin grammatical gender does not always match what an English speaker expects from the ending. A noun ending in -es is not automatically masculine or feminine just by appearance; you have to learn its gender as part of the vocabulary.

For quies, you should learn:

• quies, quietis, feminine = rest, repose, quiet

That is why the adjective is grata, not gratus or gratum.

Omnibus means to all or to everyone.

It is the dative plural of omnis, omne = all, every.

In this sentence it stands by itself, without a noun, so it means something like:

• to all people
• to everyone

This is very common in Latin: an adjective can be used on its own when the noun is understood.

Because Latin word order is much more flexible than English word order.

Placing est at the end is very normal in Latin, especially in simple statements. Latin often saves the verb for the end, although it does not have to.

So all of these are basically possible in Latin, with slightly different emphasis:

• Quies omnibus grata est
• Post longum iter quies omnibus grata est
• Quies est omnibus grata

The sentence you have is perfectly natural Latin.

The core sentence is:

• quies omnibus grata est

That breaks down as:

• quies = subject
• grata = predicate adjective
• est = verb
• omnibus = dative with grata

Then post longum iter is an added prepositional phrase telling when or under what circumstance:

• after a long journey

So the whole sentence is:

• After a long journey, rest is welcome to everyone

Because Latin has no articles.

Latin does not have separate words for:

• a / an
• the

So quies can mean:

• rest
• the rest
• a rest

and longum iter can mean:

• a long journey
• the long journey
• long journey

The exact sense is understood from context.

Yes. Gratus, -a, -um has a range of meanings depending on context, including:

• pleasing
• welcome
• agreeable
• dear

So quies omnibus grata est could be understood in slightly different but related ways, such as:

• rest is welcome to everyone
• rest is pleasing to everyone
• rest is agreeable to everyone

In this sentence, welcome or pleasing fits especially well.