مكنسة اختي في الممر جنب المدخل.

Because Arabic usually leaves out the present-tense to be in simple sentences like this.

So instead of saying X is in Y, Arabic often just says:

• X in Y

That kind of sentence is called a nominal sentence.

So:

• مكنسة أختي في الممر...
  literally works like
• My sister’s broom in the hallway...

but in natural English we translate it with is.

This is the Arabic iḍāfa structure, often called the construct phrase.

The pattern is:

• thing possessed + possessor

So:

• مكنسة اختي = broom of my sister = my sister’s broom

This is the opposite of English word order. English puts the possessor first:

• my sister’s broom

Arabic puts the possessed item first:

• broom my-sister

The suffix -ي means my.

So:

• أخت = sister
• أختي = my sister

That ending is very common in Arabic:

• أبي / أبويا = my father
• أمي = my mother
• بيتي = my house

So in this sentence, اختي is the possessor: my sister.

Because in an iḍāfa construction, the first noun normally does not take ال.

So Arabic says:

• مكنسة أختي

not:

• المكنسة أختي

Even though مكنسة has no الـ, the whole phrase is still definite, because أختي is definite (my sister is a specific person).

So the whole phrase means my sister’s broom, not just a broom of a sister.

Because ة (taa marbuuTa) often changes its pronunciation depending on position.

• When the word is said by itself, it often sounds like -a or -ah
• When it is linked to another word in an iḍāfa, it is pronounced -t

So:

• مكنسة by itself: roughly maknasa / makniseh depending on pronunciation style
• مكنسة أختي: the ending links, so you hear something like maknaset okhti

This is very normal and important to get used to.

A rough Egyptian-style pronunciation would be:

• maknaset okhti fil-mamar gamb el-madkhal

A few useful pronunciation notes:

• في الممر often sounds like fil-mamar
• جنب is usually pronounced gamb in Egyptian
• الـ is usually pronounced el- in Egyptian speech

Exact vowels can vary a bit from speaker to speaker, but that rough version will help you recognize it.

Yes, in this sentence جنب means next to / beside.

In Arabic grammar, words like جنب originally come from nouns such as side, but in actual use they often work very much like prepositions.

So:

• جنب المدخل = next to the entrance = beside the entrance

In Egyptian Arabic, this word is very commonly pronounced gamb.

Because they give two layers of location:

• في الممر = the general location
• جنب المدخل = the more exact position inside that location

So the sentence first says where the item is broadly:

• in the hallway

Then it narrows it down:

• next to the entrance

English does this too:

• It’s in the hallway, next to the entrance.

The more careful standard spelling is:

• أختي

with the hamza on the alif.

But in informal writing, people often leave hamzas off, especially in everyday typed Arabic.

So:

• اختي
  and
• أختي

are often understood the same way in casual context.

If you are writing carefully, especially for study, it is better to write:

• أختي

Yes. In Egyptian Arabic, بتاع / بتاعة / بتوع is a very common way to show possession.

So you could say:

• المكنسة بتاعة أختي

That also means my sister’s broom.

The difference is mainly structural:

• مكنسة أختي = iḍāfa structure
• المكنسة بتاعة أختي = possessive with بتاعة

Both are natural in Egyptian, but بتاعة is especially common in everyday speech.
The iḍāfa version is shorter and very common too.

Because normal Arabic writing usually leaves out short vowel marks.

So the script gives you mainly the consonants and long vowels, and the reader supplies the rest from:

• vocabulary knowledge
• grammar
• context

That is why learners often find unvoweled Arabic hard at first.

This is completely normal. In real-life Arabic, especially in dialect writing, most text appears without short vowels.

It is understandable in Egyptian, but it has a somewhat neutral / written feel because of word choice and spelling.

A few points:

• جنب would usually be pronounced gamb in Egyptian
• أختي is fine in Egyptian
• الممر and المدخل are perfectly understandable, but they can sound a bit more formal or standard than some everyday alternatives

So the sentence works well for learning, but in spontaneous speech some Egyptians might choose slightly different everyday words depending on context. The grammar pattern itself, though, is absolutely useful and important.