Jag vill ta reda på om paketet redan är på väg tillbaka.

After a modal verb like vill, Swedish normally uses a bare infinitive (no att):

• Jag vill ta reda på ...
  You do use att after many other verbs:
• Jag försöker att ta reda på ... / Jag försöker ta reda på ... (both can work, but att is common)
  With modals (kan, vill, ska, måste, får, bör) you typically don’t use att.

Ta reda på is a very common phrasal/idiomatic verb meaning to find out. Grammatically it’s built from:

• ta = take (verb)
• reda = order/clarity (noun in this fixed expression)
• på = particle/preposition in the expression

You treat ta reda på as a fixed unit in meaning, even though it’s multiple words.

Yes, redan (already) has some flexibility, but placement can affect what it “targets”:

• ... om paketet redan är på väg tillbaka. (already is on its way back — most natural)
• ... om paketet är på väg tillbaka redan. (already — with slightly more emphasis/contrast, often spoken)
• Redan usually comes before the verb in a subordinate clause, which is why redan appears before är here.

Because after om you have a subordinate clause, and Swedish subordinate clause word order typically puts sentence adverbs (like redan, inte, ofta, kanske) before the finite verb:

• ... om paketet redan är ...
  Compare:
• Main clause: Paketet är redan på väg tillbaka.
• Subordinate clause: ... om paketet redan är på väg tillbaka.

In this sentence, om means whether/if in the sense of introducing an indirect yes/no question:

• I want to find out whether the package is already on its way back.

Swedish uses om for both if and whether in these kinds of clauses; context tells you which English word sounds best.

Paket is a neuter (ett-) noun:

• Indefinite: ett paket = a package
• Definite: paketet = the package

Swedish typically expresses the by adding a suffix to the noun (and sometimes also using a separate article with adjectives).

På väg literally means on the way, and tillbaka means back. Together:

• är på väg tillbaka = is on its way back / is being returned

It’s a common, natural phrasing for something that has started the return journey or return process.

Yes, är is present tense of vara (to be). In Swedish, present tense often covers both:

• “is (right now)”
• “is (currently/these days/in progress)”

So är på väg tillbaka means the return is currently underway (not necessarily this exact second).

Yes, but there’s a nuance:

• Jag vill veta om ... = I want to know whether/if ... (focus on having the knowledge)
• Jag vill ta reda på om ... = I want to find out whether/if ... (focus on investigating/checking)

In many everyday contexts, both work, but ta reda på sounds more like you’ll check a system, call someone, look it up, etc.

A natural spoken rhythm often stresses the content words, especially the key idea:

• Jag vill ta REda på om paKETet redan är på väg tillBAka.

Also, ta REda på is often said as a single “chunk,” because it functions like one verb.

The given sentence is already very natural. A couple of common alternatives are:

• Jag vill ta reda på om paketet är på väg tillbaka redan. (slightly different emphasis on redan)
• Jag vill ta reda på om paketet redan är på väg tillbaka till avsändaren. (adds to the sender if you want to be explicit)

But the core structure—Jag vill + infinitive, then om + subordinate clause—is exactly what you’d expect in Swedish.