Ο συγκάτοικός μου κλειδώνει πάντα την πόρτα με το που φτάνει στο σπίτι.

In Greek, the usual (neutral/most common) pattern is:

• [noun] + [weak possessive pronoun] → ο συγκάτοικός μου = my roommate

Putting μου before the noun (ο μου συγκάτοικος) is generally not normal in Standard Modern Greek (it can appear in special styles/dialects, but it’s not the default).

This is an accent rule. συγκάτοικος is stressed on the antepenult (third-from-last syllable): συγκά-τοι-κος.
When a weak pronoun like μου follows a word stressed on the antepenult, Greek often adds a second accent to keep the stress “within range”:

• ο συγκάτοικος
• ο συγκάτοικός μου

You’ll see the same pattern with similar words:

• ο δάσκαλος → ο δάσκαλός μου
• ο άνθρωπος → ο άνθρωπός μου

No. συγκάτοικος is commonly used for both genders (same noun form), and the article shows the gender:

• ο συγκάτοικός μου = my (male) roommate
• η συγκάτοικός μου = my (female) roommate

(You may also hear η συγκάτοικός μου in the same accent pattern for the same reason as above.)

κλειδώνει is present tense (3rd person singular). With πάντα (always), it describes a habitual/repeated action:

• κλειδώνει πάντα = he/she always locks (it)

It’s not “right now” present; it’s the general habit.

Because την πόρτα is in the accusative case, used for the direct object (what is being locked).

• η πόρτα = the door (subject form / nominative)
• την πόρτα = the door (object form / accusative)

So: κλειδώνει (what?) την πόρτα.

με το που is an idiomatic time connector meaning as soon as / the moment that.

Structure:

• με το που + verb (usually indicative)

Here:

• με το που φτάνει = as soon as he/she arrives

It’s very common in spoken Greek and informal writing.

Greek often keeps the same “time frame” in both clauses. Since the main verb is in the present habitual (κλειδώνει πάντα), the με το που clause also uses present (φτάνει) to describe the repeated pattern:

• He always locks the door as soon as he gets home.

If you switch to the past, Greek typically switches both:

• Κλείδωσε την πόρτα με το που έφτασε στο σπίτι.
  (He locked the door as soon as he arrived home.)

στο is a contraction of σε + το:

• σε το σπίτι → στο σπίτι = at/to the house/home

This contraction is standard and extremely common:

• σε τον → στον
• σε την → στη(ν)
• σε τα → στα

It can cover both depending on the verb. With φτάνω (arrive), it naturally means arrive home / arrive at the house. In English we usually say get/arrive home rather than arrive to the house, so the best interpretation here is home.

A common pronunciation guide:

• συγκάτοικός ≈ seen-GA-tee-kos (with stress on -kos as the extra accent shows: -κός)
• The γκ is typically pronounced like ng
  • g together: [ŋg] (similar to the sound in finger, but with a clearer g).

In slower/careful speech you may hear it even more distinctly as [nɡ].