La min pardoninta amikino ridetis al mi.

Because min is the direct object of pardoni (to forgive).

In Esperanto, -n marks the direct object:

• mi = I
• min = me

So in min pardoninta, the friend is the one doing the forgiving, and me is the person being forgiven.

You can think of it as:

• pardoninta min = having forgiven me

Even though min comes before the participle here, it is still the object of pardoni.

Pardoninta is the active past participle of pardoni (to forgive).

It is built like this:

• pardon- = forgive
• -int- = having done / who did
• -a = adjective ending

So pardoninta means something like:

• having forgiven
• who had forgiven
• who forgave

In this sentence, it describes amikino:

• la min pardoninta amikino = the female friend who had forgiven me

Because it is being used like an adjective to describe amikino.

In Esperanto, participles can behave like adjectives, and adjectives end in -a.

So:

• amikino = female friend
• pardoninta amikino = a female friend who had forgiven

The participle agrees with the noun it describes, just like a normal adjective would.

If the noun were plural, it would become:

• la min pardonintaj amikinoj

If it were accusative, it would also take -n:

• Mi vidis la min pardonintan amikinon.

Yes. Amikino specifically means female friend.

• amiko = male friend or sometimes friend in a general sense, depending on context
• amikino = female friend

The suffix -in- marks female sex.

So the sentence is specifically about a female friend, not just any friend.

Because in Esperanto, adjectival modifiers normally come before the noun.

Since pardoninta is functioning like an adjective, the whole descriptive group is placed before amikino:

• la min pardoninta amikino

That literally feels a bit like:

• the me-forgiving friend

This is normal Esperanto structure.

A learner may find it more natural at first to think of the expanded version:

• La amikino, kiu pardonis min, ridetis al mi.
• The friend who forgave me smiled at me.

That version is often easier to understand, and it means essentially the same thing.

Yes, very naturally.

A very common equivalent is:

• La amikino, kiu pardonis min, ridetis al mi.

This uses a relative clause instead of a participle.

So these are roughly equivalent:

• La min pardoninta amikino ridetis al mi.
• La amikino, kiu pardonis min, ridetis al mi.

The participial version is more compact. The kiu version may feel clearer to many learners.

Because rideti takes al when you say who the smile is directed toward.

• rideti = to smile
• rideti al iu = to smile at someone

So:

• ridetis al mi = smiled at me

You do not normally use rideti with a direct object for the person receiving the smile.

La is the definite article, meaning the.

It shows that the speaker has a specific female friend in mind:

• La min pardoninta amikino = the female friend who had forgiven me

Without la, it would mean something more like:

• A female friend who had forgiven me smiled at me

So la tells us this is a particular, identifiable friend.

Because -int- marks an action that is completed before the main action, from the speaker’s point of view in the sentence.

Here:

• pardoninta = having forgiven / who had forgiven
• ridetis = smiled

So first she forgave me, and then she smiled at me.

That is why English often translates this with:

• who had forgiven me
• or simply who forgave me, depending on context

These are three active participles showing different times relative to the main idea:

• pardonanta = forgiving / who is forgiving
• pardoninta = having forgiven / who has forgiven / who had forgiven
• pardononta = about to forgive / going to forgive

So compare:

• La min pardonanta amikino = the female friend who is forgiving me
• La min pardoninta amikino = the female friend who had forgiven me
• La min pardononta amikino = the female friend who is about to forgive me

In your sentence, pardoninta shows that the forgiving is already complete.

It is correct Esperanto, but many speakers would probably find the relative-clause version more immediately natural in everyday conversation:

• La amikino, kiu pardonis min, ridetis al mi.

The participial version:

• La min pardoninta amikino ridetis al mi.

is compact and elegant, and it is fully normal Esperanto, especially in writing or in a slightly more condensed style.

So the sentence is grammatical and natural enough, but it may feel a bit denser than the more explicit kiu version.

To some extent, yes, because Esperanto has flexible word order. But some arrangements are clearer than others.

The original:

• La min pardoninta amikino ridetis al mi.

is clear once you know the structure.

A more explicit alternative is:

• La amikino, kiu pardonis min, ridetis al mi.

If you move things around too much, the sentence may become harder to parse, even if it is technically possible. So learners should usually prefer the clearest version rather than relying on word-order freedom.

Because the two forms have different grammatical roles.

• min = direct object of pardoni
• mi in al mi = object of the preposition al

In Esperanto, a preposition already marks the relationship, so you normally do not add -n after it.

So:

• min pardoninta = having forgiven me
• ridetis al mi = smiled at me

The speaker is the person forgiven, and also the person the smile is directed toward, but those are two different grammatical functions.