Мобільний оператор допоміг підключити послугу.

Because мобільний оператор is the subject of the sentence, so it is in the nominative case.

• мобільний = mobile
• оператор = operator / provider

Both words are masculine singular, so the adjective agrees with the noun:

• мобільний оператор = the mobile operator

If this noun phrase were in another case, both words would usually change:

• nominative: мобільний оператор
• genitive: мобільного оператора
• dative: мобільному оператору
• instrumental: мобільним оператором

So here the nominative is used because the operator is the one performing the action.

Допоміг is the past tense, masculine singular form of допомогти (to help, perfective).

It matches the subject оператор, which is masculine singular.

Compare:

• він допоміг = he helped
• вона допомогла = she helped
• воно допомогло = it helped
• вони допомогли = they helped

Ukrainian past tense agrees in gender and number with the subject, so допоміг is used because оператор is grammatically masculine.

This is a very common Ukrainian pattern:

• допомогти + infinitive = to help do something

So:

• допоміг підключити послугу = helped connect/activate the service

Here, підключити is an infinitive (to connect / to hook up / to activate), and it tells us what the operator helped with.

More examples:

• допоміг знайти = helped find
• допоміг зрозуміти = helped understand
• допомогла оформити документи = helped process the documents

So the structure is normal and natural.

Because after допоміг, Ukrainian usually uses the infinitive to express the action being helped.

• допоміг підключити послугу = helped connect the service
• not допоміг підключив послугу

Using підключив would make it a second finite verb, which does not fit this construction.

So:

• допоміг = the main past-tense verb
• підключити = infinitive explaining the action

This is similar to English helped connect rather than something like helped connected.

In everyday Ukrainian, підключити послугу usually means to connect, activate, or enable a service.

With mobile providers, internet, or banking, підключити often means making a service start working on your account.

Examples:

• підключити тариф = activate a plan/tariff
• підключити інтернет = connect/activate internet
• підключити послугу = activate a service

So although the basic verb can literally mean connect, in this context activate is often the most natural English translation.

Because послуга is the direct object of підключити, and with this verb it normally appears in the accusative case.

• nominative: послуга = service
• accusative: послугу = service (as the object)

So:

• підключити що? → послугу

This is a very common feminine noun pattern:

• книга → книгу
• машина → машину
• послуга → послугу

It can be followed by either, depending on the meaning.

1. допомогти + dative noun/pronoun = help someone

   • допомогти мені = help me
   • допомогти клієнту = help the customer

2. допомогти + infinitive = help do something

   • допомогти підключити послугу = help connect a service

3. It can also combine both ideas:

   • оператор допоміг мені підключити послугу = the operator helped me connect the service

In your sentence, the person being helped is not mentioned, only the action.

No, Ukrainian word order is fairly flexible, although some orders sound more neutral than others.

The neutral order here is:

• Мобільний оператор допоміг підключити послугу.

But you could also hear:

• Послугу допоміг підключити мобільний оператор.
• Допоміг підключити послугу мобільний оператор.

These alternatives change the focus or emphasis, not the core meaning.

In English, word order usually marks grammatical roles more strongly. In Ukrainian, case endings do much of that work, so word order can be freer.

Because Ukrainian infinitives do not use a separate word like English to.

The infinitive is built into the verb form itself:

• підключити = to connect / to activate
• зробити = to do
• бачити = to see

So when you see -ти (or sometimes -ть in dictionary style or older usage), that is already the infinitive form. No extra word is needed.

It can be understood either way, depending on context.

In many real-life situations, мобільний оператор means the mobile carrier/provider as a company:

• Kyivstar
• Vodafone
• lifecell

But in some contexts it may refer to an employee/operator representing the company, especially in customer service.

So the sentence could mean:

• the mobile provider helped activate the service or
• the mobile operator/customer support agent helped activate the service

Context tells you which is meant.

Because the sentence presents the action as completed.

• допоміг is perfective past: the help was successfully given
• підключити is perfective infinitive: the service was connected/activated as a completed result

This fits a situation where the task was finished.

If you wanted to talk about ongoing process or general help, you might use imperfective verbs instead, depending on context:

• допомагав підключати послугу = was helping to connect / used to help connect the service

So the perfective forms here suggest a single completed event.