Learn Hardcore Greek: Μου αρέσει να μιλάω ανοιχτά με τη φίλη μου.

αρέσει literally means "is pleasing".
The person who likes something is not the subject but an indirect object in the genitive:
- μου = to me
- σου = to you
- του / της = to him / her, etc.

So:

Μου αρέσει = It pleases me → I like it.
In this sentence, the thing that pleases you is the action να μιλάω ανοιχτά με τη φίλη μου.
That whole να… clause is the subject of αρέσει.

You do not normally say Εγώ αρέσω to mean I like.
Εγώ αρέσω would mean I am pleasing (to others), i.e. people like me.

What exactly does να do in να μιλάω? Is it like English to?

να is a particle that marks the subjunctive in Modern Greek. After να, the verb usually looks like the present tense form, but να tells you it’s in a subjunctive structure.

In English, να can correspond to:

to (when we say I like to talk)
or (that) I (when we think more literally: I like that I talk…)

Here:

μου αρέσει να μιλάω… ≈ I like to talk… / I like talking…

After να, you can choose between:

present subjunctive for ongoing / habitual action:
- να μιλάω = to be talking / to talk (generally, regularly)
aorist subjunctive for a single / complete action:
- να μιλήσω = to talk (once, to have a talk)

In this sentence, να μιλάω is used because we mean in general / habitually:
I like (in general) talking openly with my friend.

What is the difference between μιλάω and μιλώ? Are both correct?

Yes, both μιλάω and μιλώ are correct forms of the same verb μιλάω / μιλώ = to speak / to talk.

They are just two alternative present forms.
μιλάω is slightly more colloquial and very common in speech.
μιλώ sounds a bit more formal or bookish, but is also perfectly normal.

So you could also say:

Μου αρέσει να μιλώ ανοιχτά με τη φίλη μου.

No real difference in meaning here; it’s mostly style and personal preference.

What part of speech is ανοιχτά, and why is that form used?

ανοιχτά here is an adverb, meaning openly.

It comes from the adjective ανοιχτός = open.
Greek often forms adverbs from adjectives using the neuter plural form:
- καλός → καλά = good → well
- δυνατός → δυνατά = strong → strongly / loudly
- ανοιχτός → ανοιχτά = open → openly

So:

μιλάω ανοιχτά = I speak openly.

You could replace it with another adverb, for example:

μιλάω ειλικρινά = I speak honestly / sincerely,
but ανοιχτά focuses more on being open, not hiding things, not necessarily on moral honesty alone.

Why is it με τη φίλη μου and not με την φίλη μου?

The full feminine accusative article is την, but in Modern Greek:

The final -ν of την (and τον) is often dropped in everyday writing and speech before many consonants.

Common rule of thumb:

Keep -ν before vowels and certain consonants (κ, π, τ, γκ, μπ, ντ, ξ, ψ, τσ, τζ).
Drop it before most other consonants.

Since φίλη begins with φ, the article is often written and spoken as:

τη φίλη instead of την φίλη.

Both τη φίλη μου and την φίλη μου are understood, but τη φίλη μου is more common in modern, informal writing.

Why do we say τη φίλη μου and not η φίλη μου after με?

Because the preposition με (with) requires the accusative case.

η φίλη = the friend (nominative, used for the subject)
τη(ν) φίλη = the friend (accusative, used for the object)

After με, you must use accusative:

με τη(ν) φίλη μου = with my (female) friend

So:

Η φίλη μου μιλάει. = My friend is talking. (subject → nominative)
Μιλάω με τη φίλη μου. = I talk with my friend. (object of με → accusative)

Why is φίλη used here instead of φίλος?

Greek nouns have grammatical gender, and they also often match the natural gender of the person.

φίλος = (male) friend
φίλη = (female) friend

In this sentence, φίλη tells us the friend is female, so:

η φίλη μου = my (female) friend

If you wanted to say my (male) friend, you would say:

ο φίλος μου (nominative)
τον φίλο μου / το φίλο μου (accusative, after με: με τον φίλο μου)

Why does μου appear twice in the sentence, and does it mean the same thing each time?

Yes, both μου are the same form (genitive of εγώ = I), but they play different roles:

Μου αρέσει…
- μου = to me (indirect object, clitic pronoun)
- It answers: To whom is it pleasing? → to me.
…με τη φίλη μου.
- μου = my (possessive)
- It answers: Whose friend? → my friend.

Position:

As a clitic object pronoun, μου usually goes before the verb: μου αρέσει.
As a possessive, μου goes after the noun: η φίλη μου, το σπίτι μου, etc.

So the sentence literally structures as:

To me pleases to speak openly with the friend my.

Can I change the word order, for example: Μου αρέσει να μιλάω με τη φίλη μου ανοιχτά?

Yes, Greek word order is fairly flexible, especially with adverbs.

Both of these are natural:

Μου αρέσει να μιλάω ανοιχτά με τη φίλη μου.
Μου αρέσει να μιλάω με τη φίλη μου ανοιχτά.

The difference is tiny:

ανοιχτά earlier (closer to μιλάω) slightly emphasizes how you speak.
ανοιχτά at the end can sound like a final, summarizing emphasis:
I like talking with my friend – openly.

You can also slightly rearrange for emphasis:

Με τη φίλη μου μου αρέσει να μιλάω ανοιχτά.
Emphasis on με τη φίλη μου (with that person).

But you cannot move μου freely anywhere; as a clitic, it sticks to the verb group (μου αρέσει).

Could I say Μου αρέσει να μιλήσω ανοιχτά με τη φίλη μου instead of να μιλάω?

Grammatically it’s possible, but the meaning changes.

να μιλάω (present subjunctive):
- ongoing, repeated, or general action
- I like talking (in general) openly with my friend.
να μιλήσω (aorist subjunctive):
- one whole event, a single occasion
- In most contexts, Μου αρέσει να μιλήσω… sounds odd, because μου αρέσει expresses a general preference, and να μιλήσω refers to one specific talk.

You would more naturally use να μιλήσω with verbs like:

Θέλω να μιλήσω ανοιχτά με τη φίλη μου.
= I want to have an open talk with my friend (on this occasion).

So for a general like / preference, να μιλάω is the natural choice here.