Learn Hardcore Greek: Το δωμάτιό μου είναι μικρό, αλλά το τραπέζι είναι μεγάλο.

Because μου is an enclitic (unstressed) possessive. When an enclitic follows a word stressed on the antepenultimate syllable (like δωμάτιο), Greek adds a second accent on the final syllable of that word to satisfy the stress rules: το δωμάτιό μου. Writing το δωμάτιο μου is a spelling error. Compare:

ο άνθρωπός μου (extra accent; proparoxytone + enclitic)
ο φίλος μου (no extra accent; paroxytone + enclitic)

Why is there a definite article with a possessive? English just says “my room.”

In Greek you almost always keep the definite article with weak possessives: το δωμάτιό μου, η μητέρα μου, το βιβλίο σου. Dropping the article is rare and stylistic (poetry, set phrases). So “my room” is normally το δωμάτιό μου.

Why is the article το used for both nouns?

Both δωμάτιο and τραπέζι are neuter singular nouns. The nominative singular definite article for neuter is το. (Masculine uses ο, feminine η.)

Why are the adjectives μικρό and μεγάλο in those forms?

Adjectives agree with the noun in gender, number, and case, even in predicate position after είναι. Neuter singular nominative is needed here:

μικρός (m), μικρή (f), μικρό (n)
μεγάλος (m), μεγάλη (f), μεγάλο (n) Hence: μικρό, μεγάλο to match neuter δωμάτιο and τραπέζι.

Is είναι singular or plural here? Why does Greek use the same form?

είναι serves for both 3rd person singular and plural in the present. Here each clause has a singular subject, so it’s 3rd singular. Full present of είμαι:

είμαι (I am), είσαι (you are), είναι (he/she/it is),
είμαστε (we are), είστε (you are), είναι (they are).

Can I omit the second είναι and say “Το δωμάτιό μου είναι μικρό, αλλά το τραπέζι μεγάλο”?

It’s possible in very concise or stylistic Greek (headlines, notes), but in normal prose/speech you typically repeat είναι. The original with both verbs is the neutral choice.

Why the comma before αλλά? Could I use μα or όμως instead of αλλά?

A comma before αλλά is standard when joining two independent clauses. In very short phrases it’s sometimes omitted. Alternatives:

μα = but (more colloquial): ...μικρό, μα το τραπέζι...
όμως = however; it can move: ...μικρό. Όμως το τραπέζι... or ...μικρό, όμως το τραπέζι...

Where does μου go in longer noun phrases?

The weak possessive μου comes right after the first stressed word of the noun phrase—often the adjective if there is one:

Neutral: το δωμάτιό μου
With adjective: το μικρό μου δωμάτιο (most common) or το μικρό δωμάτιό μου (also correct; note the extra accent again on δωμάτιό)

How do you pronounce the tricky parts?

δωμάτιο: [ðo-MÁ-tee-o]. The δ is like the th in English “this.” In fast speech -τιο can sound like “tyo.”
τραπέζι: [tra-PE-zee].

How would I say “My room and the table are big/small” with a single verb?

Use a plural subject and make the adjective neuter plural:

Το δωμάτιό μου και το τραπέζι είναι μεγάλα/μικρά.

What are the basic plural and genitive forms of these nouns?

το δωμάτιο → plural τα δωμάτια; genitive sg. του δωματίου; genitive pl. των δωματίων. With possessive: τα δωμάτιά μου (extra accent added).
το τραπέζι → plural τα τραπέζια; genitive sg. του τραπεζιού; genitive pl. των τραπεζιών. With possessive: τα τραπέζια μου.

How do I say “my small room” versus “my room is small”?

Attributive adjective (before the noun): Το μικρό μου δωμάτιο.
Predicative adjective (after the verb): Το δωμάτιό μου είναι μικρό. Both are common, but they mean different things syntactically (attributive describes the noun; predicative makes a statement).

How do I put the sentence in the past?

Use ήταν (3rd person past of είμαι, same for singular and plural):

Το δωμάτιό μου ήταν μικρό, αλλά το τραπέζι ήταν μεγάλο.