لوحة التحكم قرب درج المكتب.

In Arabic, a present-tense sentence like this usually does not use a separate word for is.

So لوحة التحكم قرب درج المكتب literally looks like the control panel near the desk drawer, but it naturally means the control panel is near the desk drawer.

If you wanted was, will be, and so on, Arabic would normally use a verb such as كان.

It is an iḍāfa construction, often called a construct phrase.

• لوحة = panel / board
• التحكم = the control / control

Together, لوحة التحكم means control panel.

This is a very common Arabic pattern: noun + noun, where English often uses of or turns the first noun into an adjective-like modifier.

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

So Arabic says:

• لوحة التحكم

not:

• اللوحة التحكم

The whole phrase becomes definite because the second noun is definite: التحكم.
So لوحة التحكم is understood as the control panel.

Because the word ends in ة (tāʾ marbūṭa).

When a word like لوحة is said by itself, it is often pronounced roughly like lawḥa. But when it is followed by another word in an iḍāfa, the ة is pronounced as t.

So:

• by itself: لوحة
• in this phrase: لوحة التحكم = lawḥat at-taḥakkum

This is a very common feature of Arabic pronunciation.

For learners, it is often easiest to think of قرب as meaning near and functioning much like a preposition.

More technically, it is often analyzed as an adverbial noun or ẓarf of place. In either case, the important practical point is that the noun after it is in the genitive.

So here:

• قرب درج المكتب = near the desk drawer

It is another iḍāfa.

• درج = drawer
• المكتب = the desk

So درج المكتب literally means the drawer of the desk, which English would usually say as the desk drawer.

Again, notice the same pattern:

• first noun: no الـ
• second noun: definite with الـ
• whole phrase: definite

Yes, that is a good question. In unvowelled Arabic writing, درج can represent more than one word.

In this sentence, because it is followed by المكتب, the meaning is understood as drawer: desk drawer.

So context tells you which meaning is intended. Without vowels, Arabic often relies on context this way.

Because ت is a sun letter.

When الـ comes before a sun letter, the l sound is not pronounced separately. Instead, the following consonant is doubled.

So:

• التحكم is pronounced at-taḥakkum

But in المكتب, م is a moon letter, so the l is pronounced:

• المكتب = al-maktab

A likely fully vowelled version is:

لَوْحَةُ التَّحَكُّمِ قُرْبَ دُرْجِ الْمَكْتَبِ

This shows the grammar more clearly:

• لَوْحَةُ: nominative
• التَّحَكُّمِ: genitive, because it is the second part of an iḍāfa
• قُرْبَ: adverbial expression of place
• دُرْجِ: genitive after قرب
• الْمَكْتَبِ: genitive, because it is the second part of another iḍāfa

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

Yes, but the given word order is the most neutral and natural for this kind of sentence.

The sentence is basically:

• لوحة التحكم = the topic / subject
• قرب درج المكتب = the predicate, telling where it is

You could change the order for emphasis, but لوحة التحكم قرب درج المكتب is the straightforward way to say it.