الإبرة خارج الصندوق قرب ماكينة الخياطة.

Because Arabic usually leaves out the present-tense to be in simple statements.

So:

• الإبرة خارج الصندوق literally looks like the needle outside the box
• but it means the needle is outside the box

If you wanted the past or future, then Arabic would use a verb, such as كانت for was.

It is a nominal sentence.

• الإبرة = the topic/subject (the needle)
• خارج الصندوق = the main predicate/location (outside the box)
• قرب ماكينة الخياطة = an additional location phrase (near the sewing machine)

Arabic often stacks location expressions like this without needing and.

Yes. إبرة is a feminine noun.

In this sentence, that does not change much by itself, but it matters when you add adjectives or verbs:

• الإبرة صغيرة = The needle is small
• not الإبرة صغير

So it is useful to remember إبرة as feminine from the start.

خارج means outside, and in sentences like this it behaves like a noun/adverb of place rather than a simple English-style preposition.

So:

• خارج الصندوق = outside the box

It is very common in Arabic to use words like this directly before a noun:

• فوق الطاولة = above the table
• تحت الكرسي = under the chair
• خارج الصندوق = outside the box

Because in standard Arabic, خارج can connect directly to the following noun:

• خارج الصندوق = outside the box

You do not normally need من here.

If you add من, you usually change the structure or meaning, for example:

• من خارج الصندوق = from outside the box

So in your sentence, خارج الصندوق is the normal MSA pattern.

Yes. قرب here means near or close to.

So:

• قرب ماكينة الخياطة = near the sewing machine

This is a normal compact MSA structure.

You can also say:

• بالقرب من ماكينة الخياطة

That means the same thing, but it is a little more explicit in form. Both are correct.

Because this is an iḍāfa construction, often called a construct phrase.

• ماكينة الخياطة literally means machine of sewing
• naturally, it means the sewing machine

In an iḍāfa:

• the first noun usually does not take ال
• the second noun can make the whole phrase definite

So:

• ماكينة الخياطة = the sewing machine
• not الماكينة الخياطة

This is the same pattern as:

• باب البيت = the door of the house
• مفتاح السيارة = the car key

They are definite for different reasons.

• الصندوق has ال because it means the box, a specific box
• الخياطة has ال as the second part of the iḍāfa ماكينة الخياطة, which makes the whole phrase definite

Compare:

• خارج الصندوق = outside the box
• خارج صندوق = outside a box

and:

• ماكينة الخياطة = the sewing machine
• ماكينة خياطة = a sewing machine

Fully vocalized, it can be written as:

الإبرةُ خارجَ الصندوقِ قربَ ماكينةِ الخياطةِ

A simple way to read the endings is:

• الإبرةُ = nominative, because it is the subject/topic
• خارجَ = accusative as a word of place
• الصندوقِ = genitive after خارج
• قربَ = accusative as another word of place
• ماكينةِ = genitive after قرب
• الخياطةِ = genitive because it is the second noun in the iḍāfa

In normal everyday writing, these short vowels are usually omitted.

The ص in الصندوق is a sun letter, so the ل of ال is not pronounced separately.

So it is pronounced:

• aṣ-ṣundūq
• not al-ṣundūq

But الخياطة begins with خ, which is a moon letter, so there the ل is pronounced:

• al-khiyāṭa

The most natural reading is that it gives another location for the needle:

• The needle is outside the box, near the sewing machine.

If you specifically want to say that the box is the thing near the sewing machine, Arabic usually makes that clearer, for example:

• الإبرة خارج الصندوق القريب من ماكينة الخياطة
• The needle is outside the box that is near the sewing machine.

So as written, the phrase most naturally attaches to the needle’s location.