Learn Hardcore Greek: Κάθε Παρασκευή τρώω γλυκό με τη φίλη μου. - Every Friday I eat dessert with my friend female.

Παρασκευή means Friday and, like the names of the days of the week and months, it is written with a capital letter in Greek: Δευτέρα, Τρίτη, Τετάρτη, Πέμπτη, Παρασκευή, Σάββατο, Κυριακή.

So yes, when you write the name of a day as a noun (like here), you capitalize it.

Why is there no article before Κάθε Παρασκευή? Why not Κάθε τη(ν) Παρασκευή?

The word κάθε (every/each) normally goes directly before a noun without an article:

κάθε μέρα – every day
κάθε εβδομάδα – every week
κάθε Παρασκευή – every Friday

Saying κάθε την Παρασκευή is ungrammatical in modern standard Greek.
You just use κάθε + noun with no article.

Does τρώω mean “I eat” or “I am eating”? How is the present tense used here?

Modern Greek present tense covers both:

I eat (habitual, general)
I am eating (right now)

Context decides.
Here, with κάθε Παρασκευή, it clearly has a habitual meaning:

Κάθε Παρασκευή τρώω γλυκό… = I (usually / regularly) eat dessert every Friday.

So τρώω is 1st person singular, present tense, active voice of the verb τρώω (to eat).

Why is it τρώω and not τρώγω or something else?

In modern everyday Greek, the normal form is τρώω.

τρώω – standard, spoken and written modern Greek.
τρώγω – an older / more formal form; you may see it in literature or fixed expressions, but not in casual speech.

Conjugation (present):

(εγώ) τρώω – I eat
(εσύ) τρως – you eat
(αυτός/αυτή/αυτό) τρώει – he/she/it eats
(εμείς) τρώμε – we eat
(εσείς) τρώτε – you (pl./formal) eat
(αυτοί/αυτές/αυτά) τρώνε – they eat

What exactly is γλυκό here? Is it an adjective or a noun?

γλυκό can be both:

As an adjective: γλυκό παιδί – sweet child
As a noun: ένα γλυκό – a sweet, a dessert

In τρώω γλυκό, γλυκό is a neuter noun meaning dessert / something sweet.

So the sentence means: I eat dessert / I have something sweet.

Why is there no article before γλυκό? Could I say τρώω ένα γλυκό?

Both are possible, but not identical in nuance.

τρώω γλυκό
- More general: “I have dessert / I eat something sweet.”
- You focus on the type of food, not a specific item.
τρώω ένα γλυκό
- “I eat a dessert / a sweet (one dessert).”
- It sounds more like one portion / one item.

In the sentence given, τρώω γλυκό suggests a regular habit of having some kind of dessert every Friday, without specifying how many or what exactly.

What does τη φίλη μου show about gender and case? Why this form?

τη φίλη μου breaks down like this:

η φίλη – the friend (female), nominative singular
τη φίλη – the friend (female), accusative singular (direct object)
μου – my

In the sentence, τη φίλη μου is the direct object of the preposition με (with).
Prepositions in Greek take the accusative case, so:

με τη φίλη μου – with my (female) friend

Gender:

φίλη is feminine; it refers to a female friend.
The feminine definite article is η (nominative) / τη(ν) (accusative).

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

The full accusative feminine article is την.
However, in modern Greek, ν is usually dropped before certain consonants (especially φ, θ, χ, σ, ξ, ψ, π, τ, κ, μπ, ντ, γκ), particularly in speech and informal writing.

So:

την φίλη μου → τη φίλη μου
την Παρασκευή → τη Παρασκευή

Both forms are grammatically correct, but in everyday usage you normally see τη φίλη μου.
Keeping ν is more careful/formal or used for clarity in some contexts.

How does μου work here? Why isn’t it a separate word like “my friend” in English?

μου is an unstressed (clitic) possessive pronoun meaning my.
In Greek, these pronouns go after the noun:

η φίλη μου – my friend
το σπίτι μου – my house
η μητέρα μου – my mother

They do not change the form of the noun; they just attach to it.
You cannot say μου φίλη for “my friend” in normal modern Greek; you must say η φίλη μου (with the article).

In the sentence: με τη φίλη μου = with my friend.

Does φίλη mean strictly “female friend”, or can it also mean “girlfriend (romantic)”?

φίλη primarily means female friend (non-romantic by default).

It can sometimes mean “girlfriend” in a romantic sense, but that usually needs context or extra wording. For a clear romantic meaning, Greek speakers often use:

η κοπέλα μου – my girlfriend
το αγόρι μου – my boyfriend

So in a neutral sentence like Κάθε Παρασκευή τρώω γλυκό με τη φίλη μου, the most natural interpretation is simply with my female friend.

What about με? What case does it require, and can I say “with me / with him / with them” similarly?

με is the preposition with, and in modern Greek it always takes the accusative case.

Examples:

με τη φίλη μου – with my friend
με εμένα – with me
με σένα – with you
με αυτόν – with him
με αυτήν / με αυτή – with her
με αυτούς / τες / αυτά – with them (masc./fem./neut.)

In speech:

με εμένα often becomes με μένα
με εσένα often becomes με σένα

Can I change the word order? Are sentences like Με τη φίλη μου τρώω γλυκό κάθε Παρασκευή also correct?

Yes, Greek word order is relatively flexible.
Your original sentence:

Κάθε Παρασκευή τρώω γλυκό με τη φίλη μου.

Possible variants (all grammatical, with slightly different emphasis):

Τρώω γλυκό με τη φίλη μου κάθε Παρασκευή.
Με τη φίλη μου τρώω γλυκό κάθε Παρασκευή.
Γλυκό τρώω κάθε Παρασκευή με τη φίλη μου.

The neutral, most typical orders would be the original one or:

Κάθε Παρασκευή τρώω γλυκό με τη φίλη μου.
Τρώω γλυκό με τη φίλη μου κάθε Παρασκευή.

Changing the order usually shifts emphasis, not the basic meaning.

How would the sentence change if I wanted to say “with my (male) friend” or “with my friends (plural)”?

For a male friend:

Κάθε Παρασκευή τρώω γλυκό με τον φίλο μου.
- ο φίλος (nom.) → τον φίλο (acc.) – masculine

For friends (plural):

Masculine / mixed group:
- Κάθε Παρασκευή τρώω γλυκό με τους φίλους μου.
Feminine only:
- Κάθε Παρασκευή τρώω γλυκό με τις φίλες μου.

So you adjust the article and noun for gender and number, but everything else stays the same.