Он доплатил немного наличными и сохранил чек.

Доплатил means paid extra, paid the remaining amount, or topped up the payment.

It comes from the verb доплатить:

• до- = adds the idea of finishing, adding more, or bringing something up to the needed amount
• платить / заплатить = to pay

So:

• заплатил = paid
• доплатил = paid the rest / paid additionally

In this sentence, Он доплатил немного наличными suggests that some payment had already been made in another way, and then he added a little more in cash.

Доплатил is perfective, while доплачивал is imperfective.

Here the sentence describes a completed action:

• he paid a little extra
• he kept the receipt

That is why Russian uses the perfective past:

• доплатил
• сохранил

If you said доплачивал, it would sound more like:

• he was in the process of paying extra
• he used to pay extra
• he paid extra repeatedly

So доплатил fits a single finished event.

Here немного means a little / a small amount.

Because it comes with доплатил, the full idea is:

• he paid a little extra
• he added a small amount

So немного itself just means a little, but in context it naturally means a little more.

Compare:

• Он заплатил немного. = He paid a little.
• Он доплатил немного. = He paid a little extra.

Наличными is the instrumental plural form of наличные (cash).

Russian often uses the instrumental case to show the means by which something is done. In English, we often use with or just an adverb-like phrase:

• наличными = in cash / with cash

This is a very common expression:

• платить наличными = to pay in cash
• оплатить наличными = to pay in cash
• доплатить наличными = to pay the remainder in cash

Why plural? Because наличные is normally used as a plural noun meaning cash funds / cash money. So its instrumental plural is наличными.

Not in natural English. A more natural translation is:

• in cash
• with cash

But grammatically, Russian is using the instrumental case in a way that often corresponds to English expressions like:

• by...
• with...
• using...

So the literal grammar idea is something like using cash, but the best English translation is in cash.

Russian often leaves that idea understood from context.

Доплатить already contains the meaning of:

• paying what remains
• adding money to complete the payment

So you do not always need an object such as:

• остаток = the remainder
• разницу = the difference

The sentence simply says:

• Он доплатил немного наличными
  and the listener understands that he paid a bit more to complete the total.

You could make it more explicit in a longer sentence, for example:

• Он доплатил разницу наличными. = He paid the difference in cash.

But it is not necessary here.

In this context, сохранил чек most naturally means kept the receipt.

The verb сохранить can mean:

• save
• keep
• preserve

Its exact translation depends on context:

• сохранить файл = save a file
• сохранить спокойствие = keep calm
• сохранить чек = keep the receipt

So here kept is the most natural English choice.

Чек is the standard everyday Russian word for a receipt from a shop, restaurant, or similar place.

For a learner, it is useful to know:

• чек = receipt
• кассовый чек = cash-register receipt / official sales receipt

Even though check in English often means something different, Russian чек in this kind of sentence usually means receipt, not a bank check.

Because the subject is Он (he).

In Russian past tense, verbs agree with the subject in gender and number:

• доплатил = masculine singular past
• сохранил = masculine singular past

Compare:

• Он доплатил и сохранил = He paid extra and kept
• Она доплатила и сохранила = She paid extra and kept
• Они доплатили и сохранили = They paid extra and kept

So the -л ending is the normal past marker, and the masculine form here is because of он.

Because both verbs have the same subject, Russian usually states the subject once and then continues with more verbs.

So:

• Он доплатил немного наличными и сохранил чек.

means:

• He paid a little extra in cash and kept the receipt.

Repeating он would usually be unnecessary unless you wanted special emphasis:

• Он доплатил немного наличными, и он же сохранил чек.

But in normal speech and writing, one subject is enough.

The word order is fairly natural, but Russian word order is more flexible than English.

Neutral order:

• Он доплатил немного наличными и сохранил чек.

Possible variations:

• Он немного доплатил наличными и сохранил чек.
• Наличными он доплатил немного и сохранил чек.

These versions are grammatically possible, but they shift emphasis:

• немного earlier can emphasize the small amount
• наличными earlier can emphasize that the payment method was cash

So the original sentence sounds natural and neutral.

In this sentence, немного is understood to modify the action доплатил: he paid a little.

So:

• доплатил немного = paid a little extra
• наличными = in cash

Together:

• he paid a little extra, and he did so in cash

It does not mean something like a little cash in the sense of a noun phrase. If Russian wanted to say a little cash more directly as an object, the structure would usually look different.

Yes, several very useful ones:

• платить наличными = to pay in cash
• доплатить немного = to pay a little extra
• сохранить чек = to keep the receipt

These are all natural everyday combinations. If you memorize them as chunks, the sentence becomes much easier to understand and reuse.