Avus meminit se olim ex Gallia ad Italiam iter fecisse cum fideli comite.

Because meminit is one of those Latin verbs whose perfect form has a present meaning.

• meminit = he remembers
• not he remembered

This is normal for meminisse. Its forms come from the perfect stem, but in meaning they often function like a present-tense verb of remembering.

So:

• meminit = remembers
• meminerat = remembered / had remembered

This is a very common thing for learners to notice and ask about.

It is an indirect statement, also called an accusative-and-infinitive construction.

After verbs of thinking, saying, knowing, perceiving, and sometimes remembering, Latin often says:

• subject of the reported statement in the accusative
• verb of the reported statement in the infinitive

So here:

• se = the subject of the reported action, in the accusative
• fecisse = the infinitive verb

Together, se ... iter fecisse means:

• that he made a journey
• or more naturally in English here, that he once traveled

Because se is the reflexive pronoun, and it refers back to the subject of the main verb, which is avus.

So:

• Avus meminit se ... fecisse = Grandfather remembers that he himself did ...

If Latin used eum, that would normally mean some other man, not the grandfather himself.

So se shows that the person who remembers and the person who traveled are the same person.

Because the traveling happened before the remembering.

In indirect statement, the tense of the infinitive shows time relative to the main verb:

• present infinitive = same time
• perfect infinitive = earlier time
• future infinitive = later time

Here the grandfather now remembers a journey that happened long ago, so Latin uses the perfect infinitive:

• fecisse = to have made / to have done

So meminit se ... iter fecisse means:

• he remembers that he made the journey
• literally, he remembers himself to have made the journey

Literally, iter facere means to make a journey.

• iter = journey, route, march
• facere = to make, to do

But as an idiom, iter facere often simply means:

• to travel
• to go on a journey

So iter fecisse can be translated very naturally as:

• to have traveled
• to have made a journey

This is a very common Latin expression.

Because the sentence expresses two different ideas of movement:

• ex Gallia = out of / from Gaul
• ad Italiam = to / toward Italy

The prepositions match those meanings:

• ex takes the ablative
• ad takes the accusative

So:

• Gallia is ablative singular after ex
• Italiam is accusative singular after ad

Latin is being very precise:

• starting point: ex Gallia
• destination: ad Italiam

Yes, it could have, but the nuance is slightly different.

• ad Italiam = to Italy, toward Italy
• in Italiam = into Italy, often with more emphasis on entering

In many contexts both can be translated simply as to Italy, but ad often focuses on the destination in a general way, while in can stress motion into the place.

So ad Italiam is perfectly normal here.

Because cum meaning with takes the ablative case.

So:

• cum comite = with a companion
• cum fideli comite = with a faithful companion

Both words are ablative singular:

• comite = ablative singular of comes, comitis
• fideli = ablative singular of fidelis, agreeing with comite

This is the regular Latin construction for accompaniment.

Olim means something like:

• once
• formerly
• long ago

In this sentence it tells us that the journey happened in the past, and probably quite some time ago.

So se olim ... iter fecisse means:

• that he once traveled ...
• that he long ago made a journey ...

It is an adverb, so it does not change form.

For English, yes; for Latin, not really.

Latin word order is much more flexible than English word order. The sentence is organized by meaning and emphasis rather than by a fixed subject-verb-object pattern.

Here the main structure is:

• Avus meminit = main clause
• se ... iter fecisse = indirect statement
• cum fideli comite = accompanying phrase

A more mechanically arranged version might be:

• Avus meminit se olim iter ex Gallia ad Italiam cum fideli comite fecisse.

But the original order is perfectly natural Latin.

Because Latin does not have articles like English the or a/an.

So:

• avus can mean grandfather, a grandfather, or the grandfather
• Gallia = Gaul
• Italia = Italy

The context tells you how definite the noun is. In this sentence, English naturally says Grandfather or the grandfather, but Latin does not need a separate word for that.