Незважаючи на невеликий платіж, банк перевіряє підозрілу операцію.

Yes. Literally, незважаючи comes from a verb meaning not looking / not paying attention, so word-for-word незважаючи на is something like without looking at.

But in modern Ukrainian, this expression is very commonly used idiomatically to mean:

• despite
• in spite of

So in this sentence, Незважаючи на невеликий платіж... means Despite the small payment...

It functions like a fixed expression, so learners usually just remember незважаючи на + accusative.

Because незважаючи на takes the accusative case.

So the noun phrase after it must be accusative:

• невеликий платіж = a small payment

Here, both words look the same as the nominative form, but that is normal because:

• платіж is a masculine inanimate noun
• in the singular, masculine inanimate nouns often have the same nominative and accusative form
• the adjective невеликий also matches that pattern here

So although it looks like nominative, grammatically it is accusative because of незважаючи на.

Because this opening phrase functions like an introductory adverbial phrase: Despite the small payment, ...

In Ukrainian, such phrases are normally separated by a comma when they come at the beginning of the sentence.

So:

• Незважаючи на невеликий платіж, банк перевіряє підозрілу операцію.

is the standard punctuation.

Because банк is the subject of the sentence — the thing doing the action.

The verb is перевіряє = checks / is checking, and the bank is the one performing that action.

So:

• банк = nominative subject
• перевіряє = verb
• підозрілу операцію = direct object

Перевіряє is present tense, third person singular:

• (він/вона/воно) перевіряє = he/she/it checks or is checking

In Ukrainian present tense, the same form can often correspond to either:

• checks (habitual/general present)
• is checking (action happening now)

Which one sounds better in English depends on context.

Here, both are possible:

• The bank checks the suspicious transaction
• The bank is checking the suspicious transaction

Very often, English would prefer is checking if this is a specific situation happening now.

Because Ukrainian normally uses the imperfective verb for the present tense.

Перевіряти / перевіряти (imperfective) gives forms like:

• перевіряю
• перевіряє
• перевіряють

A perfective verb in Ukrainian does not normally have a true present meaning like English present. Its “present” forms usually refer to the future.

So if you want to say is checking / checks, imperfective is the normal choice.

Because підозрілу операцію is the direct object, so it must be in the accusative case.

The dictionary/basic form is:

• підозріла операція = a suspicious operation/transaction
  nominative singular

But after the verb перевіряє (checks), it becomes accusative:

• підозрілу операцію

For feminine singular nouns and adjectives, the accusative ending changes clearly:

• підозріла → підозрілу
• операція → операцію

Yes, операція can mean several things depending on context:

• operation (medical or military, etc.)
• procedure
• transaction in banking/finance

In this sentence, because we have банк and платіж, операція clearly means a financial transaction.

So підозріла операція here is best understood as:

• a suspicious transaction

Both relate to small size, but невеликий is often the more natural choice for things like amount, size, or degree in neutral everyday language.

So:

• невеликий платіж = a small payment
  very natural

малий can also mean small, but it can sound less idiomatic in some contexts, or more like literal physical smallness, depending on usage.

For amounts of money, payments, sums, fees, etc., невеликий is very common.

Yes. Ukrainian word order is fairly flexible, although different orders can sound more or less natural depending on emphasis.

The given sentence is very natural:

• Незважаючи на невеликий платіж, банк перевіряє підозрілу операцію.

You could also say:

• Банк перевіряє підозрілу операцію, незважаючи на невеликий платіж.

That version puts the main statement first and the despite phrase later. It is still understandable, but the original version sounds especially natural if you want to foreground the contrast.

No. In this meaning, the normal expression is:

• незважаючи на + accusative

So you need на:

• незважаючи на невеликий платіж

Without на, it would be ungrammatical for this meaning.

They are very close in meaning. Both can mean:

• despite
• in spite of

So you could also say:

• Попри невеликий платіж, банк перевіряє підозрілу операцію.

That is also natural.

A learner can think of them as near-equivalents in many sentences, though style and preference may differ a bit depending on context.

The sentence suggests a contrast:

• the payment is small
• but the bank is still checking the transaction because it seems suspicious

So the focus is not just the facts, but the idea that a small amount does not stop the bank from investigating.

That contrast is exactly what незважаючи на highlights.