Κάθε μέρα ο συμφοιτητής μου μιλάει ελληνικά μαζί μου στο φροντιστήριο.

Κάθε μέρα means every day and expresses a habitual action.

In Greek, time expressions like κάθε μέρα, σήμερα, αύριο, το βράδυ can appear:

• at the beginning: Κάθε μέρα ο συμφοιτητής μου μιλάει…
• in the middle: Ο συμφοιτητής μου κάθε μέρα μιλάει…
• at the end: Ο συμφοιτητής μου μιλάει… κάθε μέρα.

All are grammatically correct; changing the position mostly affects emphasis, not basic meaning. Starting with Κάθε μέρα emphasizes the frequency of the action.

In Greek, nouns very often take a definite article (ο, η, το) even when English does not use the.

• ο συμφοιτητής μου = literally the classmate my → my classmate

Using the article with a possessed noun (noun + μου/σου/του…) is the normal pattern in Greek. Leaving the article out (συμφοιτητής μου) is possible in some contexts (headings, very informal speech, certain fixed expressions), but here ο συμφοιτητής μου is the natural, standard form.

Greek possessive pronouns normally come after the noun, and they are unstressed “little words” (clitics):

• ο συμφοιτητής μου = my classmate
• το βιβλίο σου = your book
• η φίλη του = his friend

Putting μου before the noun (μου συμφοιτητής) is not normal modern Greek. Instead, stress-shifted forms like εμένα, εσένα (meaning “me, you” with emphasis) come before for contrast:

• ο δικός μου συμφοιτητής = my classmate (as opposed to someone else’s)

Yes, ο συμφοιτητής is masculine: (male) classmate (at university).

The feminine form is:

• η συμφοιτήτρια = (female) classmate

Plural forms:

• οι συμφοιτητές μου = my (male / mixed) classmates
• οι συμφοιτήτριές μου = my female classmates

In mixed groups, Greek usually defaults to the masculine plural οι συμφοιτητές.

Both μιλάει and μιλά are 3rd person singular present of μιλάω/μιλώ = to speak.

• μιλάει = more “full” form, very common in speech
• μιλά = shorter form, common in both speech and writing

Meaning is the same: he/she speaks / is speaking.

So in this sentence you could also say:

• …ο συμφοιτητής μου μιλά ελληνικά…

Both are correct; learners can safely use μιλάει or μιλά interchangeably.

Modern Greek present tense covers both English simple present and present continuous. So:

• μιλάει can mean he speaks or he is speaking, depending on context.

Because the sentence has Κάθε μέρα, it clearly describes a habitual action:

• Κάθε μέρα ο συμφοιτητής μου μιλάει…
  = Every day my classmate speaks / is speaking…

English prefers speaks for habits here, but Greek just uses the plain present.

ελληνικά is the neuter plural form of the adjective ελληνικός, -ή, -ό (Greek). In this use, it functions as a noun meaning (the) Greek language:

• μιλάω ελληνικά = I speak Greek
• μαθαίνω ελληνικά = I’m learning Greek

This “neuter plural as language name” is very common:

• αγγλικά = English
• γαλλικά = French
• ιταλικά = Italian

You would see η ελληνική (γλώσσα) in more formal contexts, e.g.:

• η ελληνική γλώσσα = the Greek language (formal / descriptive)

μαζί μου literally means together with me, and in practice it just means with me:

• μιλάει ελληνικά μαζί μου = he speaks Greek with me

You could also say:

• μιλάει ελληνικά με μένα = he speaks Greek with me

Differences:

• μαζί μου is more idiomatic here; very common and neutral.
• με μένα slightly emphasizes me (as opposed to someone else).

So for a simple “with me,” μαζί μου is the best choice in this sentence.

στο is a contraction of σε + το:

• σε = in / at / to / on (general preposition)
• το = the (neuter singular article)

So:

• στο φροντιστήριο = σε + το φροντιστήριο = at the tutoring school

Similar contractions:

• σε + τον → στον (e.g. στον φίλο μου)
• σε + την → στη(ν) (e.g. στη δουλειά)
• σε + τους → στους
• σε + τις → στις

το φροντιστήριο is not a regular state school. It’s a private tutoring center / cram school, often for:

• extra classes after normal school
• exam preparation
• foreign language lessons

So στο φροντιστήριο here likely means at the (language) tutoring center or at the cram school, not at a normal primary/secondary school (σχολείο) or university (πανεπιστήμιο).

Yes. Greek word order is flexible, especially for adverbs and time expressions.

All of these are grammatical:

• Κάθε μέρα ο συμφοιτητής μου μιλάει ελληνικά μαζί μου στο φροντιστήριο.
• Ο συμφοιτητής μου κάθε μέρα μιλάει ελληνικά μαζί μου στο φροντιστήριο.
• Ο συμφοιτητής μου μιλάει κάθε μέρα ελληνικά μαζί μου στο φροντιστήριο.

The differences are mainly about emphasis:

• Early Κάθε μέρα = emphasizes every day
• Early ο συμφοιτητής μου = emphasizes my classmate as the topic

Greek is a pro-drop language: subject pronouns (εγώ, εσύ, αυτός, etc.) are often omitted because the verb ending already shows the person and number.

• μιλάει already tells you he/she/it (3rd singular), and context makes it clear it’s ο συμφοιτητής μου.

You use the pronoun αυτός when you need extra emphasis or contrast:

• Αυτός μιλάει ελληνικά, όχι εγώ.
  He is the one who speaks Greek, not me.

In your sentence, the neutral, natural form is without αυτός.

Approximate pronunciation (stressed syllable in caps):

• Κάθε μέρα → KA-the ME-ra
• ο συμφοιτητής → o sim-fo-i-ti-TIS (the οι is like ee, so more like sim-fi-ti-TIS)
• μου → moo
• μιλάει → mi-LA-i (sounds like mi-LA-ee; in fast speech often close to mi-LÁ in rhythm)
• ελληνικά → e-li-ni-KA
• μαζί μου → ma-ZI moo
• στο φροντιστήριο → sto fron-di-STI-rio

Key points:

• αι is pronounced like e in get (here in μιλάει, spelling is -άει, but modern pronunciation is close to μιλά).
• οι is pronounced like ee in see.
• Stress is very important in Greek; it can distinguish words, so pay attention to the accented syllables.