יש עוד ארגזים במחסן, אבל במרתף כבר אין מקום.

They are the standard Hebrew words for existence:

• יש = there is / there are
• אין = there isn’t / there aren’t / there is no

So:

• יש עוד ארגזים במחסן = there are more boxes in the storage room
• אין מקום = there is no room / no space

In present-tense Hebrew, this is the normal way to say that something exists or does not exist somewhere.

No. יש does not change for singular or plural.

You say:

• יש ארגז = there is a box
• יש ארגזים = there are boxes

And similarly:

• אין ארגז = there is no box
• אין ארגזים = there are no boxes

So יש and אין are fixed forms in this kind of sentence.

Here עוד means more or additional.

So יש עוד ארגזים means there are more boxes or there are additional boxes.

A useful thing to know: עוד can also mean still or again in other contexts, depending on where it appears and what it modifies. But in this sentence, before the noun ארגזים, it means more/additional.

עוד ארגזים usually means additional boxes.

יותר ארגזים often sounds more comparative, like more boxes than something/someone else.

So:

• יש עוד ארגזים במחסן = there are more/additional boxes in the storage room
• יש יותר ארגזים במחסן could suggest there are more boxes in the storage room than elsewhere / than before / than in another place

In this sentence, עוד is the most natural choice.

The singular is ארגז = box / crate.

It is a masculine noun:

• singular: ארגז
• plural: ארגזים

The ending ־ים is the regular masculine plural ending in Hebrew.

Because מקום here means room / space, not places.

In this kind of sentence, Hebrew usually uses singular מקום to mean available space:

• אין מקום = there is no room / no space

If you said אין מקומות, that would usually mean there are no places/spots/seats, which is a different idea.

So אין מקום is exactly what Hebrew normally says for there’s no room.

כבר means already or by now.

So כבר אין מקום literally means there is already no room.

In natural English, this is often translated as:

• there’s already no room
• there’s no room anymore
• there’s no longer any room

It gives the idea that the basement has reached its limit.

Hebrew word order is flexible, and fronting במרתף helps create a contrast:

• במחסן ... but במרתף ...

So the sentence highlights the difference between the two locations:

• in the storage room, there are still more boxes
• but in the basement, there is already no space

You could also say אבל כבר אין מקום במרתף, and that would still be understandable. But starting with במרתף makes the contrast stronger.

It may be built into the form.

The prefix ב־ means in. When it combines with the definite article ה־ (the), the result is written as one word:

• ב + המחסן → במחסן
• ב + המרתף → במרתף

So these forms can mean:

• in the storage room
• in the basement

A tricky point: in normal unpointed Hebrew spelling, במחסן and במרתף can also look the same as in a storage room and in a basement. Context tells you which meaning is intended.

In pronunciation, definite forms are often heard as:

• ba-machsan
• ba-martef

Because Hebrew normally uses אין for negative existence.

So:

• יש מקום = there is room
• אין מקום = there is no room

Using לא here would not be the standard way to express this idea. לא usually negates ordinary verbs, while אין is the normal negative partner of יש in existential sentences.

A common pronunciation is:

Yesh od argazim ba-machsan, aval ba-martef kvar ein makom.

Approximate stress:

• argaZIM
• machSAN
• aVAL
• marTEF
• maKOM

That can help you hear the rhythm of the sentence more naturally.