Learn Hardcore Dutch: Bij de klantenservice zeiden ze dat het pakket bij het afhaalpunt ligt, en er is nog een extra aanbieding. - At customer service they said the package is at the pickup point, and there is another special offer.

Dutch main clauses obey the verb-second (V2) rule. If you put something other than the subject in first position (here, the prepositional phrase Bij de klantenservice), the finite verb must still be in second position, so the subject ze comes after the verb:

First position: Bij de klantenservice
Second position (finite verb): zeiden
Subject: ze

Without fronting, you could also say: Ze zeiden bij de klantenservice dat .... Starting with Bij de klantenservice puts topical emphasis on the location.

Why is it past in the main clause (zeiden) but present in the dat-clause (ligt)?

Dutch often keeps the present tense in reported speech when the statement is still true now. So:

Zeiden = they said (in the past)
... dat het pakket ... ligt = that the package is (still) there now

If you use lag instead of ligt, you imply it was there at that past moment, with no claim about the current situation:

Gisteren zeiden ze dat het pakket bij het afhaalpunt lag (it was there then; maybe not now).

What does bij convey in bij de klantenservice? Why not op, in, or van?

bij = at, with (a person/desk/department): bij de klantenservice, bij de dokter.
op is used with some institutions (e.g., op kantoor) or surfaces, but op de klantenservice is odd.
in means inside a space: in de winkel (inside the store). bij de klantenservice refers to the counter/department, not being physically inside something.
van means of/from and doesn’t mean at: van de klantenservice would mean belonging to customer service.

Who are ze here? Can I use zij instead?

Ze is the unstressed form of zij and here means an indefinite they (the people working at customer service). Zij is the stressed/contrastive form. You can say Bij de klantenservice zeiden zij ... to emphasize that it was they (as opposed to someone else).

How does word order work after dat?

In a dat-clause, the finite verb goes to the end:

dat + subject + (objects/adverbials) + finite verb
Example: ... dat het pakket bij het afhaalpunt ligt.

Avoid ... dat het pakket ligt bij het afhaalpunt in careful Dutch; keep the finite verb at the end.

Why ligt for a package? Could I say is or staat?

Dutch uses specific position verbs:

liggen (ligt) = lies/is lying (flat/resting). Natural for a package: Het pakket ligt ...
staan (staat) = stands (upright), also used for items listed/printed.
zijn (is) = neutral existence/location. ... dat het pakket bij het afhaalpunt is is acceptable and neutral, but ligt sounds idiomatic in logistics (e.g., Het pakket ligt klaar).

What exactly is afhaalpunt, and why het?

afhaalpunt is a compound: afhalen (to pick up) + punt (point) → pickup point.
It’s a neuter noun: het afhaalpunt, plural de afhaalpunten.
Synonyms you may see: servicepunt, pakjespunt. Ophaalpunt exists but is less common.

Why het pakket and not de pakket?

Pakket is a neuter noun, so it takes het: het pakket, plural de pakketten. Gender isn’t always predictable; you learn it with the noun.

Is the comma before en required?

No. In Dutch, a comma before en between two main clauses is optional. It’s often used for readability or to separate longer clauses, as in the sentence here.

What is er doing in er is nog een extra aanbieding?

Er is an expletive (dummy subject) used in existential sentences, equivalent to English there in there is/are. You normally need it: Er is nog een extra aanbieding. Without er, it sounds unnatural: Is nog een extra aanbieding is not good standard Dutch.

Does nog mean still or another here? What about nog een vs een andere?

nog can mean still/yet, but with a numeral or een it means another/one more.
nog een = another, an additional one: Er is nog een extra aanbieding = there is an additional special offer.
een andere = a different one (contrast, not necessarily additional).
nog steeds = still (continuing state).

What’s the difference between aanbieding, korting, actie, deal, and aanbod?

aanbieding: a special offer (often a product temporarily cheaper or bundled).
korting: a discount (percentage/amount off).
actie: a promotion/campaign (can include various deals or conditions).
deal: informal/marketing for a bargain or agreement.
aanbod: the offer/assortment (what’s on offer generally), not a specific discounted item.

Are there other correct ways to order the whole sentence?

Yes. For example:

Ze zeiden bij de klantenservice dat het pakket bij het afhaalpunt ligt, en er is nog een extra aanbieding.
You can also add ook for emphasis in the second clause (see next question). Avoid in a dat-clause: ... dat het pakket ligt bij het afhaalpunt; keep the finite verb at the end.

Should I add ook in the second clause to mean also?

You can, but you don’t have to. Nog already implies addition. All of these are fine, with slightly different emphasis:

... en er is nog een extra aanbieding. (neutral additional info)
... en er is ook nog een extra aanbieding. (explicit also; a bit more emphatic)

Does bij de klantenservice mean physically at the desk or the department/people?

It can mean either, depending on context:

Physical location: at the customer service desk/counter.
Institutional/agentive: the customer service department (the staff) said so. In this sentence, it naturally reads as the staff at customer service being the source.