Мобільний інтернет працює повільно.

Because it has to agree with інтернет in gender, number, and case.

• інтернет is masculine
• it is singular
• here it is in the nominative case (the basic dictionary form, used for the subject)

So the adjective also takes the masculine singular nominative form:

• мобільний інтернет

If the noun changed, the adjective would change too:

• мобільна мережа = mobile network
• мобільне покриття = mobile coverage

Because it is the subject of the sentence — the thing performing the action.

In Мобільний інтернет працює повільно, the mobile internet is what works / operates slowly, so інтернет stays in the nominative.

A very literal structure is:

• Мобільний інтернет = subject
• працює = works / operates
• повільно = slowly

Yes — this is very natural in Ukrainian.

The verb працювати basically means to work / to function / to operate. It is often used for machines, devices, systems, apps, websites, and connections.

So Мобільний інтернет працює повільно means something like:

• mobile internet is working slowly
• the mobile internet connection is slow
• the mobile internet is functioning slowly

This is a normal Ukrainian way to talk about technical performance.

Працює is the 3rd person singular present tense form of the verb працювати.

Conjugation in the present tense:

• я працюю = I work
• ти працюєш = you work
• він / вона / воно працює = he / she / it works
• ми працюємо = we work
• ви працюєте = you work
• вони працюють = they work

Since інтернет is singular and treated as it, Ukrainian uses працює.

Because повільно is an adverb, while повільний is an adjective.

• повільний = slow (describes a noun)
• повільно = slowly (describes a verb)

Here it describes how the internet works:

• працює повільно = works slowly

Compare:

• Повільний інтернет = slow internet
• Інтернет працює повільно = the internet works slowly

English learners often mix these up because English uses slow in some informal contexts, but Ukrainian keeps the adjective/adverb distinction more clearly here.

Yes, you can, but it is slightly different in nuance.

• Мобільний інтернет працює повільно = the mobile internet is functioning slowly right now / in this situation
• Мобільний інтернет повільний = mobile internet is slow / the mobile internet is slow as a quality or general description

So:

• працює повільно focuses more on performance
• повільний focuses more on a property or description

Both are possible, but the original sentence sounds especially natural when talking about a connection that is currently underperforming.

Ukrainian does not have articles like a or the.

So Мобільний інтернет can mean:

• mobile internet
• the mobile internet

The exact meaning depends on context.

This is something English speakers need to get used to: Ukrainian usually leaves definiteness unstated unless context makes it clear.

Yes. Ukrainian word order is more flexible than English word order, although not completely free.

The neutral, standard order here is:

• Мобільний інтернет працює повільно.

You could also hear:

• Повільно працює мобільний інтернет.
• Мобільний інтернет повільно працює.

These alternatives change the focus or emphasis a bit:

• putting повільно earlier emphasizes slowly
• the original order is the most neutral and textbook-like

For learners, the original sentence is the safest default.

A simple approximate pronunciation is:

• moh-BEEL-nyi een-tehr-NET prah-TSYU-yeh poh-VIL-noh

A few helpful notes:

• льн in мобільний is softer than an English l
• працює has цює, which can be tricky; try something like tsyu-ye
• stress is roughly:
  • мобільний
  • інтернет
  • працює
  • повільно

If you want to sound more natural, pay special attention to the soft consonants and to not reducing vowels as much as in English.

Мобільний інтернет is completely normal and common.

Depending on context, Ukrainians might also say:

• інтернет на телефоні = internet on the phone
• мобільні дані = mobile data
• зв’язок поганий = the connection is bad
• погано ловить інтернет = the internet signal is bad / reception is poor

But мобільний інтернет працює повільно is a clear, natural sentence and easy to understand.

Because in modern Ukrainian, інтернет is normally treated as a common noun, not a proper name.

So lowercase інтернет is standard in ordinary writing:

• інтернет працює
• підключення до інтернету

You may still see uppercase Інтернет in some older texts or stylistic usage, but lowercase is the normal modern choice.