في بيتنا غرفة كبيرة، وفي الغرفة نافذة قريبة من المطبخ.

Arabic often starts a nominal sentence with a prepositional phrase (جارّ ومجرور) to set the scene. Here في بيتنا (“in our house”) comes first, and the “real” subject comes after it: غرفةٌ كبيرةٌ (“a big room”).
This is a very common pattern: في + place + thing = “There is … in …”.

Arabic frequently expresses “there is/there are” without any extra word. The structure في بيتنا غرفةٌ already implies existence.
You can add هناك for emphasis or clarity: هناك غرفةٌ كبيرةٌ في بيتنا (“There is a big room in our house”), but it’s not required.

بيتنا means our house. It’s formed from:

• بيت = “house”
• ـنا = the attached pronoun meaning “our / us”

So بيت + نا → بيتنا.

In Arabic, adjectives typically come after the noun they describe:

• غرفةٌ كبيرةٌ = “a big room” (noun + adjective)

Putting the adjective first is unusual in straightforward description and usually creates a different, marked style.

غرفة is feminine largely because it ends with ـة (tā’ marbūṭa), which is a common marker of feminine nouns.
Because it’s feminine, the adjective must also be feminine: كبيرة (not كبير).

• غرفةٌ كبيرةٌ is introducing the room for the first time, so it’s indefinite: “a big room”.
• Then the sentence refers back to that same room, so it becomes definite: الغرفة = “the room”.

This is similar to English: a room… the room…

Yes, و is “and”. Here it links two related statements: 1) في بيتنا غرفة كبيرة
2) وفي الغرفة نافذة قريبة من المطبخ

Using و + في… is a very common way to continue describing locations: “And in the room…”

Because it’s introducing the window for the first time, it’s indefinite:

• نافذةٌ = “a window”

If you were talking about a specific, already-known window, you could say:

• في الغرفة النافذةُ… = “In the room, the window…” (more specific/definite)

قريبة means “near/close” (feminine to match نافذة).
Arabic commonly uses the pattern:

• قريب/قريبة من + noun = “close to + noun”

So قريبة من المطبخ = “close to the kitchen”.
(من here is the standard preposition used with “close/near” in this construction.)

In many contexts, English uses “the” differently from Arabic. In a home, “the kitchen” is often understood as a specific, known place, so Arabic naturally uses the definite form:

• المطبخ = “the kitchen”

You can make it indefinite (مطبخ) if you mean “a kitchen” in a more general/unspecified sense, but in a typical house-description, the kitchen is expected.

In fully vocalized MSA, you might see:

• في بيتِنا (بيتِ = genitive because of في)
• غرفةٌ كبيرةٌ (often nominative in this kind of nominal sentence)
• في الغرفةِ (genitive after في)
• نافذةٌ قريبةٌ (often nominative)
• من المطبخِ (genitive after من)

In most everyday writing, these vowel endings are omitted, but the grammar still assumes them.