Post longa serĉado mi trovis mian pasporton en la valizo.

In Esperanto, adjectives end in -a. So longa means long as an adjective describing serĉado.

Adjectives also agree with the noun they describe in number and case. Here serĉado is singular and not accusative, so longa stays simple:

• longa serĉado = a long search / long searching

If the noun changed, the adjective would change too:

• longaj serĉadoj = long searches
• longan serĉadon = a long search as a direct object

The suffix -ad- often adds the idea of an ongoing, repeated, or extended action.

So:

• serĉo = a search
• serĉado = searching, search activity, the process of searching

In this sentence, serĉado suggests that the searching took some time. Post longa serĉo would also be possible, but post longa serĉado emphasizes the drawn-out activity a bit more.

Because post is a preposition, and nouns after prepositions normally do not take the accusative just for being after the preposition.

So:

• post longa serĉado = after a long search

The -n ending is not used here. In Esperanto, accusative after a preposition is mainly used with location prepositions to show movement toward something, such as:

• en la valizo = in the suitcase
• en la valizon = into the suitcase

Esperanto has no indefinite article. English a/an is usually just left out.

So:

• longa serĉado can mean a long search
• la longa serĉado would mean the long search

Esperanto only has one article, la, which means the.

Because -is is the past-tense verb ending in Esperanto.

Common verb endings are:

• -as = present
• -is = past
• -os = future
• -us = conditional
• -u = command / wish

So mi trovis means I found.

A useful point for English speakers: the verb does not change for person:

• mi trovis
• li trovis
• ili trovis

All of them use trovis.

Because mian pasporton is the direct object of trovis: it is the thing that was found.

In Esperanto, the direct object takes -n, and any adjective or possessive that agrees with it also takes -n.

So:

• mia pasporto = my passport
• mian pasporton = my passport as a direct object

Here mia behaves like an adjective, so it changes too.

Because en la valizo shows location, not movement.

With place prepositions in Esperanto:

• no -n = location
• -n = motion toward / into

So:

• en la valizo = in the suitcase
• en la valizon = into the suitcase

In this sentence, the passport was located inside the suitcase when it was found, so en la valizo is correct.

Because la means the, and the sentence is talking about a specific suitcase.

Esperanto uses la when the speaker expects the listener to know which thing is meant, either from context or from the situation. Here it is most naturally understood as the suitcase relevant to the situation.

Without la, en valizo would sound much more general, more like in a suitcase or in suitcases as a kind of place, which is probably not the intended meaning.

Yes, that is the normal understanding.

Just like in English, a phrase like en la valizo can in theory attach to different parts of the sentence, but in normal use people understand it as telling you where the passport was found: the passport was in the suitcase.

If someone wanted to make that extra explicit, they could say something like:

• Mi trovis mian pasporton, kiu estis en la valizo.

But the original sentence is completely natural.

Yes. Esperanto word order is fairly flexible because endings show grammatical function.

The original order is neutral and natural:

• Post longa serĉado mi trovis mian pasporton en la valizo.

But you could also say:

• Mi trovis mian pasporton en la valizo post longa serĉado.
• En la valizo mi trovis mian pasporton.
• Mian pasporton mi trovis en la valizo.

These versions mainly change emphasis, not the core meaning.

The letter ĉ is pronounced like ch in church.

Esperanto stress is always on the next-to-last syllable.

So these words are pronounced like this:

• ser-ĈA-do
• TRO-vis
• mi-AN
• pas-POR-ton
• va-LI-zo

That regular stress pattern is one of the very helpful things about Esperanto pronunciation.