Learn Hardcore Dutch: Bij de douane laat ik mijn paspoort en visum zien.

In Dutch main clauses the finite verb must occupy the second position (V2 word order). Since the sentence starts with the adverbial phrase Bij de douane, the verb laat comes next (second), and the subject ik follows.

What does bij de douane exactly mean?

Bij means “at” or “by,” and de douane means “the customs (office/authority).” Together, Bij de douane translates as “at customs.”

Why do we use laten zien instead of just zien?

Zien simply means “to see,” whereas laten zien is a causative construction meaning “to show” (literally “to let [someone] see”). You use laten zien when you want to express that you display something for someone else.

Why is there no aan before de douane (as in “aan de douane”)?

Here bij de douane indicates location (“at customs”). If you were showing your passport directly to a person (e.g. a customs officer), you would use aan:
Ik laat mijn paspoort àán de douanebeambte zien.
But when you simply state where the action takes place, you use bij.

Why doesn’t mijn appear twice (before paspoort and visum)?

When two nouns share the same possessive adjective, you need it only once: mijn paspoort en visum. Repeating it (mijn paspoort en mijn visum) is grammatically possible but less natural.

Could you also say Ik laat mijn paspoort en visum zien bij de douane? How flexible is the word order?

Yes. You can move the location to the end:
Ik laat mijn paspoort en visum zien bij de douane.
Dutch allows adverbials (time, manner, place) in different positions, but the finite verb must remain immediately after the subject if nothing else precedes it.

Can you use tonen instead of laten zien here?

Absolutely. Tonen means “to show” and works as a simple transitive verb:
Bij de douane toon ik mijn paspoort en visum.
Both tonen and laten zien are common; laten zien is a light-verb construction, tonen is the single verb equivalent.