Упаковка залишиться, якщо тільки продавець не попросить її відправити.

Yes. Залишиться is the perfective future form of залишитися.

In this sentence, it means will remain / will stay.

A useful contrast is:

• залишатися = imperfective, to remain / to keep remaining
• залишитися = perfective, to remain / to end up staying

So:

• Упаковка залишиться = The packaging will remain
• This sounds like a single future result, which is why the perfective form fits well.

Also, the -ся form is normal here. Залишитися often means to remain, stay, be left rather than something literally reflexive like leave oneself.

In this sentence, якщо тільки ... не works like unless.

So:

• якщо тільки продавець не попросить... = unless the seller asks...

This is a very common thing that confuses English speakers, because Ukrainian often uses не in structures where English would already express the negative idea through a word like unless.

So even though English says:

• unless the seller asks

Ukrainian says, literally:

• if only the seller does not ask

But the actual meaning in context is simply unless the seller asks.

No. On its own, якщо тільки can have other meanings depending on context, such as:

• if only
• provided that
• as long as

But in a sentence like this, especially with не after it, it commonly gives the meaning unless:

• якщо тільки ... не ... = unless ...

So here you should understand the whole chunk together, not word by word.

Because the sentence is talking about a future possibility.

• попросить is the perfective future of попросити
• It means will ask

So:

• продавець не попросить = the seller does not ask / will not ask

In English, after unless, we often use the present tense:

• unless the seller asks

But Ukrainian is more straightforward here and uses a future form when the meaning is future.

Її here is the accusative singular form of вона and refers back to упаковка.

Since упаковка is feminine singular, the matching object pronoun is:

• її = her / it

In this sentence it means it:

• попросить її відправити = asks for it to be sent

For feminine nouns, the accusative often looks like the genitive if the noun is animate, but with pronouns you just learn the pronoun form directly. Here the important point is that її is the direct object referring to упаковка.

The sentence leaves that unstated.

Literally, it is something like:

• asks for it to be sent

Ukrainian often allows this kind of construction without naming the person who will perform the action. The focus is on the request and on the packaging being sent, not on exactly who sends it.

Depending on context, the understood meaning could be:

• the seller asks someone to send it
• the seller requests that it be sent
• the seller asks for it to be shipped

So the sentence is intentionally a bit impersonal.

Because Ukrainian often uses попросити + infinitive to mean ask to do something.

Examples:

• попросити допомогти = to ask someone to help
• попросити зачекати = to ask someone to wait

Here:

• попросить її відправити

literally looks like will ask to send it, but in smoother English it is usually understood as:

• will ask for it to be sent
• will ask to have it sent

So the infinitive is completely normal after попросити.

Both orders are possible in Ukrainian.

Ukrainian word order is more flexible than English, because case endings and verb forms do a lot of the grammatical work. That means word order often reflects focus, emphasis, or just natural rhythm.

So:

• попросить її відправити
• попросить відправити її

can both be grammatical, though they may sound slightly different in emphasis.

The version in your sentence sounds natural and keeps її closely linked to the earlier noun упаковка.

Usually упаковка means packaging, packing, or the package/wrapping material, depending on context.

That is important because English speakers may first think of package as the item being shipped. But упаковка is more about the packing/packaging itself.

So in this sentence, it likely means that the packaging will stay or be kept, unless the seller asks for it to be sent.

The exact English translation depends on the wider situation:

• packaging
• the packaging
• sometimes the box/packing

Because не is just part of the clause, not something that needs its own punctuation.

The main structure is:

• Упаковка залишиться,
• якщо тільки продавець не попросить її відправити.

The comma separates the main clause from the subordinate clause introduced by якщо тільки.

Inside that subordinate clause, не попросить is simply the normal verb phrase will not ask.

Yes. A more straightforward version could be:

• Упаковка залишиться, якщо продавець не попросить її відправити.

or even:

• Упаковка залишиться, якщо продавець не попросить відправити її.

These are a bit more direct.

The original with якщо тільки ... не adds a stronger unless / except if nuance. It can sound slightly more formal or more carefully framed than the simplest version.