Bij een zoekgeraakt pakket is de levertijd onbekend.

Here bij means something like in the case of, when dealing with, or for in a general situational sense.

So:

• Bij een zoekgeraakt pakket = In the case of a lost package
• not literally next to a lost package

That is a very common use of bij in Dutch when talking about situations, conditions, or categories:

• Bij slecht weer blijven we binnen. = In bad weather, we stay inside.
• Bij kinderen werkt deze methode goed. = For children / With children, this method works well.

So in your sentence, bij introduces the situation under discussion.

Both can be possible in Dutch, but zoekgeraakt is especially common for things like mail, packages, luggage, documents, and other items that have gone missing.

There is a slight nuance:

• zoekgeraakt = gone missing, become lost
• verloren = lost

With a package, zoekgeraakt often sounds very natural because it suggests that somewhere in the delivery process, the package has disappeared from track or cannot currently be found.

Also, zoekgeraakt comes from the verb zoekraken, which means to get lost or to go missing.

So:

• een zoekgeraakt pakket = a package that has gone missing
• een verloren pakket is understandable, but often less idiomatic in this context

This is a very common Dutch adjective-ending question.

In Dutch, an adjective before a noun usually takes -e, but there is one important exception:

No -e with:

• an indefinite article (een)
• a singular
• a het-word

Here:

• pakket is a het-word
• it is singular
• it has een

So you get:

• een zoekgeraakt pakket

Compare:

• het zoekgeraakte pakket
• een zoekgeraakt pakket

Once the noun becomes definite, the -e appears:

• het zoekgeraakte pakket = the lost package

This same pattern happens with many adjectives:

• een groot huis
• het grote huis

Grammatically, it is functioning like an adjective before the noun pakket.

Historically, it comes from a verb form: the past participle of zoekraken. But in this sentence it behaves adjectivally:

• een zoekgeraakt pakket

This is very common in Dutch. Past participles are often used like adjectives:

• een gestolen fiets = a stolen bike
• een gesloten deur = a closed door
• een beschadigd product = a damaged product

So while zoekgeraakt is built from a verb, in this sentence it works as an adjective describing the package.

Because levertijd is a de-word.

Dutch compound nouns take their gender from the last part of the compound. Here:

• levertijd = lever-
  • tijd
• tijd is a de-word
• so levertijd is also a de-word

That is why the sentence says:

• de levertijd

Compare:

• de tijd
• de wachttijd
• de levertijd

The final element determines the article.

This is an example of normal Dutch V2 word order in a main clause.

Dutch main clauses usually put the finite verb in the second position. The first position can be filled by different kinds of information, not only the subject.

Here the sentence begins with the prepositional phrase:

• Bij een zoekgeraakt pakket

That takes the first position. Because of that, the finite verb is must come next:

• Bij een zoekgeraakt pakket is ...

Then comes the subject:

• de levertijd

And then the rest:

• onbekend

So the structure is roughly:

• [Situation] + [finite verb] + [subject] + [complement]

You could also say:

• De levertijd is bij een zoekgeraakt pakket onbekend.

That is grammatically possible, but the original sentence sounds more natural if you want to frame the whole statement as applying specifically to the case of a lost package.

Yes. Onbekend is an adjective meaning unknown.

In this sentence it is used predicatively, meaning it comes after is and describes the subject:

• de levertijd is onbekend

This is parallel to English:

• The delivery time is unknown

Compare other Dutch examples:

• De deur is open.
• Het antwoord is duidelijk.
• De oorzaak is onbekend.

So is onbekend is not a special verb phrase; it is simply to be + adjective.

Both can relate to something being lost, but they are used differently.

• kwijt usually means lost / no longer having / unable to find
• zoekgeraakt means gone missing / become lost

Examples:

• Ik ben mijn sleutels kwijt. = I’ve lost my keys / I can’t find my keys.
• Het pakket is zoekgeraakt. = The package has gone missing.

With packages and formal delivery situations, zoekgeraakt is especially common and sounds more idiomatic than kwijt.

You might hear:

• Uw pakket is zoekgeraakt.

More naturally than:

• Uw pakket is kwijt.

The second is understandable, but less standard in formal shipping language.

Usually bij is the best choice here.

• bij een zoekgeraakt pakket = in the case of a lost package

If you use voor, it may sound more like for in the sense of intended for or applicable to, and it is less natural in this sentence.

If you use van, that would suggest possession or relation of a different kind, as in the delivery time of a package, but here the point is the situation of a package being lost, not ownership.

So:

• Bij een zoekgeraakt pakket is de levertijd onbekend. = natural
• Voor een zoekgeraakt pakket is de levertijd onbekend. = possible in some contexts, but less idiomatic here
• Van een zoekgeraakt pakket is de levertijd onbekend. = awkward in this meaning

So a learner should treat bij here as the normal Dutch choice for in the case of.

Yes, but then it is no longer simply an adjective before the noun; it is part of the verbal idea zoekraken.

Compare:

• een zoekgeraakt pakket = a lost / missing package
• het pakket is zoekgeraakt = the package has gone missing

So the same form can appear in two related ways:

1. Attributive: before a noun

   • een zoekgeraakt pakket

2. As part of the verb phrase

   • het pakket is zoekgeraakt

That is why learners sometimes feel it is halfway between an adjective and a verb form. In practice, that intuition is not wrong.