Post longam horam breve spatium otii discipulis valde gratum est.

The subject is breve spatium otii.

You can tell because:

• est is singular
• gratum is also singular and neuter
• spatium is a singular neuter noun, so gratum agrees with it

So the basic structure is:

breve spatium otii ... gratum est
= a short period of rest ... is welcome/pleasant

discipulis is not the subject; it is in the dative and means to the students.

Because post takes the accusative when it means after.

So:

• post = after
• longam horam = a long hour in the accusative, because it is the object of the preposition

This is not the accusative of duration here; it is simply the case required by post.

Because spatium is a neuter noun, and the adjective has to agree with it.

• spatium = neuter singular
• the neuter singular nominative of brevis, breve is breve

So:

• masculine/feminine: brevis
• neuter: breve

That is why Latin says breve spatium.

Otii is the genitive singular of otium.

It depends on spatium and tells you a space/period of what?
Answer: of leisure, of rest

So spatium otii means something like:

• a period of rest
• a span of leisure
• a break

This is a very normal Latin way to connect two nouns, where English often uses of.

Because gratus commonly takes the dative of the person to whom something is pleasing, welcome, or agreeable.

So:

• gratum est discipulis = it is welcome to the students
• more naturally in English: the students are very glad of it or it is very welcome to the students

This is a very common Latin pattern:

something + gratus/grata/gratum + dative + est

Gratum is a predicate adjective used with est.

It agrees with spatium, which is:

• singular
• neuter

So the adjective must also be:

• singular
• neuter

Hence gratum est, not grata est or gratus est.

The phrase means is welcome / is pleasing / is agreeable.

Valde modifies gratum.

It is an adverb meaning very, so:

• gratum est = is welcome / pleasing
• valde gratum est = is very welcome / very pleasing

Latin often places an adverb close to the adjective or verb it modifies, and that is what is happening here.

Because Latin word order is much freer than English word order.

This sentence is arranged for emphasis and flow, not because each word must stay in that exact place.

A rough breakdown is:

• Post longam horam = setting the time first: after a long hour
• breve spatium otii = the main thing being talked about
• discipulis = tells you to whom
• valde gratum est = finishes with the idea is very welcome

Latin uses endings to show grammatical function, so it does not rely on word order as much as English does.

Yes. Latin often puts est at the end, and that would still be perfectly normal.

For example, Post longam horam breve spatium otii discipulis valde gratum est and a version with est at the very end are both understandable Latin.

The position of est is flexible. Moving it can slightly change emphasis or rhythm, but not the basic meaning.

Because Latin has no articles.

So a noun like spatium can mean:

• a period
• the period

depending on context.

Likewise discipulis can mean to the students, and English has to choose the most natural wording. Latin leaves that to context rather than using separate words like a/an/the.