المفتاح بين الكرسي والطاولة.

Because this is a present-tense nominal sentence in Arabic. In sentences like The key is between the chair and the table, Arabic usually does not use a separate word for is.

So:

• المفتاح = the key
• بين الكرسي والطاولة = between the chair and the table

Together, that naturally means The key is between the chair and the table.

If you wanted was, Arabic would normally use كان.

بين means between, and sometimes among, depending on context.

In this sentence, بين introduces the location of the key:

• بين الكرسي والطاولة = between the chair and the table

After بين, the following nouns are treated as objects of a preposition, so in fully vocalized formal Arabic they are in the genitive case.

In Arabic, if both nouns are definite, you normally put الـ on each one:

• الكرسي = the chair
• الطاولة = the table

So Arabic says literally:

• between the chair and the table

You do not usually say one الـ and let it cover both nouns.

This is the most straightforward order for a simple nominal sentence:

• المفتاح = the topic / subject
• بين الكرسي والطاولة = the comment / predicate

So the structure is basically:

• The key
  • between the chair and the table

Arabic can sometimes move the prepositional phrase earlier for emphasis, but the given order is very natural and common.

Yes. In traditional grammar, المفتاح is the مبتدأ (the thing being talked about), and بين الكرسي والطاولة is the خبر (what is being said about it).

So:

• المفتاح = the subject/topic
• بين الكرسي والطاولة = the predicate/information about it

Because و meaning and is written as a prefix in Arabic. It attaches directly to the next word, with no space:

• والطاولة = and the table

This is completely normal in Arabic spelling. Many short particles do this.

Because ط is a sun letter. When الـ comes before a sun letter, the l sound of الـ is not pronounced, and the next consonant is doubled.

So:

• الطاولة is pronounced
• aṭ-ṭāwila

But it is still written with الـ.

A simple pronunciation, without full case endings, is:

al-miftāḥ bayna al-kursī waṭ-ṭāwila

A more careful fully inflected reading could be something like:

al-miftāḥu bayna al-kursīyi waṭ-ṭāwilati

In normal printed Arabic, the short vowels and case endings are usually not written, so learners often first meet it as:

المفتاح بين الكرسي والطاولة

In fully vocalized MSA, the sentence would typically be read with case:

• المفتاحُ — nominative, because it is the subject/topic
• بينَ — usually pronounced with fatḥa
• the nouns after بين are in the genitive

So the idea is:

• المفتاحُ بينَ الكرسيِّ والطاولةِ

In ordinary writing, these endings are usually omitted.

Yes, but the meaning changes.

• المفتاح = the key
• مفتاح = a key

So:

• المفتاح بين الكرسي والطاولة = The key is between the chair and the table
• مفتاح بين الكرسي والطاولة = A key is between the chair and the table or There is a key between the chair and the table, depending on context

Not very much in this specific sentence.

• المفتاح is masculine
• الطاولة is feminine
• الكرسي is masculine

But since there is no adjective or verb agreeing with these nouns here, you do not see much gender effect in the sentence itself.

Gender would matter more if you added an adjective, for example:

• الطاولة الكبيرة = the big table
• الكرسي الكبير = the big chair

Not always. بين often means between with two things, as in this sentence, but it can also be used more broadly in the sense of among or among the things/people depending on context.

Here, because there are exactly two reference points:

• the chair
• the table

the best translation is clearly between.

Yes. مفتاح comes from the root ف ت ح, which is related to opening.

It is on a common noun pattern that often gives the name of a tool or instrument. So مفتاح originally has the sense of that which opens, which is why it means key.

This is useful because Arabic vocabulary often works through roots and patterns, not just isolated words.