شاشة الحاسوب في المكتب كبيرة، لكن شاشة هاتفي صغيرة.

In Arabic, the present tense often uses a nominal sentence, so there is usually no separate word for is.

So:

• شاشة الحاسوب في المكتب كبيرة literally = The computer screen in the office big
• natural English = The computer screen in the office is big

The same is true for:

• شاشة هاتفي صغيرة = My phone screen is small

If you wanted was or will be, Arabic would normally use a verb such as كان or سيكون.

Because شاشة is a feminine singular noun.

A very common sign of a feminine noun in Arabic is the ending ة (tāʾ marbūṭa), and شاشة has that ending.

Arabic adjectives and predicate adjectives must agree with the noun in:

• gender
• number
• usually definiteness when they are regular attributive adjectives

So:

• شاشة ... كبيرة = screen ... big (feminine singular)
• شاشة ... صغيرة = screen ... small (feminine singular)

If the noun were masculine, you would expect:

• كبير
• صغير

instead.

Because both expressions are iḍāfa constructions, often translated as X of Y or Y’s X.

So:

• شاشة الحاسوب = the screen of the computer / the computer screen
• شاشة هاتفي = the screen of my phone / my phone screen

In an iḍāfa:

• the first noun usually does not take ال
• the second part determines whether the whole phrase is definite

That means:

• شاشة الحاسوب is definite because الحاسوب is definite
• شاشة هاتفي is definite because a noun with a possessive suffix like -ي (my) is definite

So even without ال on شاشة, the whole phrase can still mean the ....

هاتفي is made of:

• هاتف = phone
• -ي = my

So:

• هاتف = a phone / phone
• هاتفي = my phone

Then:

• شاشة هاتفي = the screen of my phone = my phone screen

This possessive suffix system is very common in Arabic:

• كتابي = my book
• بيته = his house
• سيارتنا = our car

The final ة is called tāʾ marbūṭa.

As a general rule:

• when you stop on the word by itself, it is usually pronounced like -a
• when the word is connected grammatically to what follows, it can sound like -t

So:

• شاشة by itself: shāsha
• شاشة الحاسوب in an iḍāfa: shāshat al-ḥāsūb (or in full case ending style, shāshatu al-ḥāsūbi)

This is normal and happens with many feminine nouns.

في المكتب means in the office.

It is a prepositional phrase:

• في = in
• المكتب = the office

It gives location information. In this sentence, it most naturally helps describe the first screen/computer phrase:

• شاشة الحاسوب في المكتب = the computer screen in the office

Arabic often leaves a little flexibility about exactly what the phrase attaches to, and context tells you what is meant.

Also, after a preposition like في, the following noun is grammatically in the genitive case. In fully vowelled Arabic that would be المكتبِ.

لكن means but or however.

It contrasts the two parts of the sentence:

• شاشة الحاسوب في المكتب كبيرة
• لكن شاشة هاتفي صغيرة

So the whole idea is:

• The computer screen in the office is big, but my phone screen is small.

You may also later meet the related form لكنّ in grammar study. It is connected in meaning, but it behaves a little differently syntactically. For this sentence, the easiest understanding is simply but.

Here it is functioning as the predicate of the sentence.

In other words:

• شاشة الحاسوب في المكتب = the subject
• كبيرة = what is being said about it

So كبيرة means big, but in this sentence it works like is big because Arabic leaves out the present-tense is.

The same applies to:

• صغيرة = small
• in context: is small

So these are adjective forms, but they are doing the job of the sentence predicate.

One careful fully vowelled reading is:

شَاشَةُ الحَاسُوبِ فِي المَكْتَبِ كَبِيرَةٌ، لَكِنْ شَاشَةُ هَاتِفِي صَغِيرَةٌ.

A helpful transliteration is:

shāshatu al-ḥāsūbi fī al-maktabi kabīratun, lakin shāshatu hātifī ṣaghīratun.

In most normal Arabic writing, these short vowels and case endings are omitted, which is why the original sentence appears without them.

Yes.

That is because:

• ح in الحاسوب
• م in المكتب

are both moon letters, so the ل of ال is pronounced:

• al-ḥāsūb
• al-maktab

If the word began with a sun letter, the ل would assimilate instead. For example, الشاشة is pronounced more like ash-shāsha, not al-shāsha.

So in this sentence, you do pronounce the l in both الحاسوب and المكتب.