الأسطوانة الإسفنجية والكرة الطبية قرب بساط التمرين.

Because this is a present-tense nominal sentence in Arabic.

In Modern Standard Arabic, when you say something like:

• The foam roller and the medicine ball are near the exercise mat

the verb to be is usually not written or spoken in the present tense.

So:

• الأسطوانة الإسفنجية والكرة الطبية قرب بساط التمرين

literally looks like:

• The foam roller and the medicine ball near the exercise mat

but it naturally means:

• The foam roller and the medicine ball are near the exercise mat.

If you wanted the past or future, then Arabic would normally use a verb such as كان or سيكون.

Because in Arabic, an adjective must match the noun it describes in definiteness.

So:

• الأسطوانة الإسفنجية = the foam roller
• الكرة الطبية = the medicine ball

Here, both nouns are definite because they have الـ, so the adjectives must also be definite:

• الأسطوانة → الإسفنجية
• الكرة → الطبية

If the nouns were indefinite, the adjectives would also be indefinite:

• أسطوانة إسفنجية = a foam roller
• كرة طبية = a medicine ball

This matching is very important in Arabic adjective phrases.

These are feminine adjectives, and they are agreeing with feminine nouns:

• أسطوانة is feminine
• كرة is feminine

So the adjectives must also be feminine:

• إسفنجي → masculine

• إسفنجية → feminine

• طبي → masculine
• طبية → feminine

Also, both of these are the kind of adjectives often called nisba adjectives, formed from a noun:

• إسفنج = sponge / foam
  → إسفنجي / إسفنجية = sponge-like / foam
• طب = medicine
  → طبي / طبية = medical

So الكرة الطبية literally means the medical ball, which is the standard Arabic way to say medicine ball.

Because this is an iḍāfa construction, often called a genitive construction or noun-noun phrase.

• بساط التمرين literally means mat of exercise
• In natural English, that becomes exercise mat

In an iḍāfa:

1. the first noun usually does not take الـ
2. the second noun determines whether the whole phrase is definite

So:

• بساط تمرين = an exercise mat
• بساط التمرين = the exercise mat

Even though بساط itself has no الـ, the whole phrase is definite because التمرين is definite.

That is why بساط التمرين can mean the exercise mat.

قرب here functions as an expression of place meaning near.

In grammar terms, it is often treated as a ẓarf makān (adverbial expression of place), originally a noun meaning nearness/closeness.

So:

• قرب بساط التمرين = near the exercise mat

A learner may expect something like قريب من, because that is also common:

• قريب من بساط التمرين = near the exercise mat

Both patterns exist, but they are structured differently:

• قرب + noun
• قريب من + noun

So in this sentence, قرب is not an adjective agreeing with the subject; it is an adverbial/location expression.

Because قرب is a simple, compact way to say near without making the predicate agree in gender and number.

If you used an adjective instead, it would have to agree with the two items being described.

Since the subject is:

• الأسطوانة الإسفنجية والكرة الطبية

that is two feminine singular nouns joined by و, so an agreeing adjective would normally be dual feminine:

• الأسطوانة الإسفنجية والكرة الطبية قريبتان من بساط التمرين

That means:

• The foam roller and the medicine ball are near the exercise mat

So:

• قرب بساط التمرين = uses an adverbial expression
• قريبتان من بساط التمرين = uses an agreeing adjective

Both are possible, but قرب avoids the extra agreement.

Because ط and ت are sun letters.

With sun letters, the ل of الـ is not pronounced; instead, the following consonant is doubled.

So:

• الطبية is pronounced roughly aṭ-ṭibbiyya
• التمرين is pronounced roughly at-tamrīn

But with words beginning with a moon letter, the ل is pronounced normally. For example:

• الكرة = al-kura
• الإسفنجية = al-isfanjiyya

So in this sentence you hear a mix:

• al-ustuwaana
• al-isfanjiyya
• wal-kura
• aṭ-ṭibbiyya
• qurb
• bisāṭ
• at-tamrīn

A fully vocalized version would be:

الأُسْطُوانَةُ الإِسْفِنْجِيَّةُ وَالْكُرَةُ الطِّبِّيَّةُ قُرْبَ بِساطِ التَّمْرِينِ.

The main case endings are:

• الأُسْطُوانَةُ — nominative
• الإِسْفِنْجِيَّةُ — nominative, matching the noun
• الْكُرَةُ — nominative
• الطِّبِّيَّةُ — nominative, matching the noun
• قُرْبَ — accusative as an adverbial expression of place
• بِساطِ — genitive
• التَّمْرِينِ — genitive

In normal everyday Arabic writing, these endings are usually not written, but it is useful to know them for grammar.

Yes, in careful Modern Standard Arabic it is understandable and natural enough, especially in educational or descriptive contexts.

Literally:

• أسطوانة = cylinder / roller-shaped object
• إسفنجية = foam / sponge-like

So الأسطوانة الإسفنجية literally means something like:

• the foam cylinder
• the foam roller

That is a good descriptive MSA phrase for the exercise item called a foam roller in English.

Likewise:

• الكرة الطبية literally = the medical ball
• natural English = the medicine ball

Arabic often names modern objects this way: a literal or descriptive phrase that matches the function of the item.

Because Arabic is listing two separate noun phrases:

• الأسطوانة الإسفنجية
• الكرة الطبية

Each one is its own complete definite phrase, so each one keeps its own الـ.

That is very normal in Arabic:

• الكتاب والقلم = the book and the pen
• الطاولة والكرسي = the table and the chair

So in your sentence, Arabic is not treating this as one combined unit with a single article. It is simply joining two definite noun phrases with و = and.