Ми не змінили ні тарифного плану, ні мобільного оператора.

It means neither ... nor.

So:

• ні тарифного плану
• ні мобільного оператора

together mean neither the tariff plan nor the mobile operator.

This is a very common Ukrainian pattern for linking two negative alternatives.

Yes, it is a kind of double negative, but that is normal and correct in Ukrainian.

Ukrainian commonly uses:

• не with the verb
• and ні ... ні with the items being negated

So:

• Ми не змінили ні тарифного плану, ні мобільного оператора.

literally has the structure:

• We did not change neither X nor Y

But in natural English, you translate it as:

• We changed neither X nor Y
• or We didn’t change either X or Y

English usually avoids this kind of multiple negation in standard usage, but Ukrainian does not.

Because after a negated verb, Ukrainian often uses the genitive instead of the accusative for the direct object.

Here the verb is negated:

• не змінили = did not change

So the objects appear in the genitive:

• тарифного плану
• мобільного оператора

Compare:

• Ми змінили тарифний план. = We changed the tariff plan.
  
  • тарифний план = accusative (same as nominative for an inanimate masculine noun? Actually here it changes according to case pattern: nominative/accusative singular is тарифний план)
• Ми не змінили тарифного плану. = We did not change the tariff plan.
  
  • тарифного плану = genitive

This genitive after negation is a very important pattern to notice.

Good question. This noun can be a little misleading.

Оператор refers to a person/company category treated grammatically like an animate masculine noun, and for animate masculine nouns, the accusative singular often looks the same as the genitive singular.

So:

• Ми змінили мобільного оператора.
• Ми не змінили мобільного оператора.

Both can look the same on the noun phrase.

That means this part of the sentence does not visibly show the negation-related case change as clearly as тарифного плану does.

So for learners:

• тарифний план → тарифного плану clearly shows accusative vs. genitive
• мобільного оператора may look identical in both contexts

Змінили is:

• past tense
• plural
• from the verb змінити = to change

Because the subject is ми (we), the verb takes the plural past form:

• я змінив / змінила
• ти змінив / змінила
• ми змінили

So:

• Ми змінили = We changed
• Ми не змінили = We did not change

This is mainly a matter of aspect.

• змінити = perfective → to change, to make the change, to complete the action
• змінювати = imperfective → to be changing, to change in a general/repeated/ongoing sense

In this sentence, the speaker is talking about the result: no change was made. That is why the perfective verb змінити fits well.

So:

• Ми не змінили ... = We did not change ... / We haven’t changed ...

If you used an imperfective form, it would shift the nuance toward process, habit, or repeated action.

Because the whole noun phrase has to change case.

The dictionary form is:

• тарифний план = nominative singular

But after negation here, it becomes genitive singular:

• тарифного плану

Both words change:

• тарифний → тарифного
• план → плану

This is normal adjective-noun agreement: the adjective must match the noun in case, number, and gender.

Yes, that is usually a very good way to think about it.

A practical matching is:

• не + ні ... ні
  = not + either ... or = neither ... nor

For example:

• Він не п’є ні чаю, ні кави.
  = He drinks neither tea nor coffee.

So in your sentence:

• Ми не змінили ні тарифного плану, ні мобільного оператора.
  = We changed neither the tariff plan nor the mobile operator.

Yes, normally yes.

When ні ... ні connects two coordinated parts, Ukrainian usually puts a comma before the second part:

• ні тарифного плану, ні мобільного оператора

This is the standard punctuation pattern in a sentence like this.

Yes, Ukrainian word order is fairly flexible, though some orders sound more natural than others.

The original order is neutral and clear:

• Ми не змінили ні тарифного плану, ні мобільного оператора.

You might also encounter variations for emphasis, for example:

• Ні тарифного плану, ні мобільного оператора ми не змінили.

This puts stronger focus on the two things that were not changed.

But for learners, the original sentence is the best neutral model.

They are very similar in meaning: both can mean neither ... nor.

However:

• ні ... ні is the most common and neutral choice
• ані ... ані can sound more emphatic, formal, or literary in some contexts

For everyday learning, ні ... ні is the pattern to master first.

Ми is in the nominative case, because it is the subject of the sentence.

• ми = we

So the sentence structure is:

• Ми = subject
• не змінили = verb
• ні тарифного плану, ні мобільного оператора = objects under negation

A natural positive version would be:

• Ми змінили тарифний план і мобільного оператора.

That means We changed the tariff plan and the mobile operator/provider.

Notice the difference:

With negation:

• не змінили ні тарифного плану, ні мобільного оператора

Without negation:

• змінили тарифний план і мобільного оператора

The most noticeable case change is:

• тарифний план → тарифного плану

That contrast helps show the genitive-after-negation pattern.