Completo el formulario aduanero y la declaración aduanera.

Here completo is a verb, not an adjective. It is the first-person singular present tense of completar:

• yo completo = I complete / I fill out

So in this sentence, Completo el formulario aduanero y la declaración aduanera means I fill out the customs form and the customs declaration.

As an adjective, completo can also mean complete/full, but that is not what is happening here.

Spanish often omits subject pronouns when they are not needed, because the verb ending already shows who the subject is.

• completo = I complete
• completas = you complete
• completa = he/she/you formal completes

So Completo... already tells you the subject is I. Adding yo is possible, but it is usually only done for emphasis or contrast.

• Yo completo el formulario, y tú firmas. = I fill out the form, and you sign.

Because the nouns have different grammatical genders:

• formulario is masculine → el formulario
• declaración is feminine → la declaración

In Spanish, articles must match the gender of the noun:

• el for masculine singular
• la for feminine singular

This is grammatical gender, so it does not mean the objects are actually male or female.

Because adjectives in Spanish usually agree in gender and number with the noun they describe.

• formulario is masculine singular → aduanero
• declaración is feminine singular → aduanera

So:

• el formulario aduanero
• la declaración aduanera

This is a very common pattern in Spanish.

In Spanish, adjectives often come after the noun, especially when they are classifying or descriptive in a factual way.

So Spanish says:

• formulario aduanero
• literally, form customs-related

rather than putting the adjective first like English usually does:

• customs form
• customs declaration

This noun + adjective order is very normal in Spanish.

They are related, but they are not exactly the same word.

• formulario = form
• declaración = declaration / statement

So:

• formulario aduanero = customs form
• declaración aduanera = customs declaration

In real travel contexts, these may refer to paperwork you complete for customs, and sometimes the distinction depends on the country or situation.

Yes, llenar is also very common, and in many situations it may sound even more natural for forms.

Both can work:

• Completo el formulario = I complete the form
• Lleno el formulario = I fill out the form

In much of Latin America, llenar un formulario is extremely common in everyday speech. Completar is also correct and widely understood.

Yes. Completo is the present indicative.

It can mean things like:

• I fill out the customs form and the customs declaration
• I am filling out the customs form and the customs declaration
  (depending on context)
• I fill out as a habitual action, if the context suggests repetition

Spanish present tense is often broader than English simple present.

Spanish normally uses y for and.

It changes to e only before a word that begins with an i sound:

• padre e hijo
• España e Italia

Here the next word is la, so there is no reason to change it:

• el formulario aduanero y la declaración aduanera

So y is correct.

Usually, in a sentence like this, Spanish keeps both adjectives because each noun has its own adjective agreement:

• el formulario aduanero y la declaración aduanera

That is the clearest and most natural full version.

Sometimes context can allow less repetition, but for learners it is best to keep both. You cannot simply use one adjective at the end for both nouns here, because one noun is masculine and the other is feminine.

Yes. Both are possible.

• complete is a more direct match for completar
• fill out is often the most natural English translation for forms and paperwork

So both of these work:

• I complete the customs form and the customs declaration.
• I fill out the customs form and the customs declaration.

In everyday English, fill out often sounds more natural with documents.

A very useful rule is that nouns ending in -ción are generally feminine.

Examples:

• la declaración
• la información
• la nación
• la conversación

So when you see declaración, you can usually predict:

• la declaración
• declaración aduanera

This is a helpful pattern to remember.