Learn Hardcore Icelandic: Ég á bankakort.

að eiga (ég á…) = to own/possess something as yours. That’s what you want for a card you own.
að hafa (ég hef…) = to have in a broad or formal sense; common in set phrases (e.g., hef áhuga “have interest”, hef tíma “have time”). It’s not the everyday choice for owning physical items.
að vera með (ég er með…) = to have with you/at hand. Use this for “I have a bank card on me.”

So: Ég á bankakort = I own a bank card; Ég er með bankakort = I have a bank card with me right now.

What case is bankakort in, and why?

The verb að eiga takes a direct object in the accusative. Bankakort is neuter; in the singular, nominative and accusative look the same, so you see bankakort either way. Other singular cases:

Dative: bankakorti
Genitive: bankakorts

How do I say “the bank card” or “my bank card”?

Icelandic adds the definite article as a suffix:

“the bank card” = bankakortið
“my bank card” = bankakortið mitt There’s no separate word for the indefinite article “a/an,” so plain bankakort already means “a bank card.”

How do I make it plural, and how do I say “I have two bank cards”?

Neuter nouns like bankakort don’t change in the nominative/accusative plural:

Plural (indefinite): bankakort
Plural (definite): bankakortin Examples:
Ég á tvö bankakort. (two)
Ég á þrjú bankakort. (three)
Ég á fjögur bankakort. (four) Note the neuter numerals: eitt bankakort, tvö, þrjú, fjögur.

Does Ég á bankakort also mean “I have a bank card with me right now”?

Not necessarily. Ég á bankakort speaks about ownership. If you mean “on me/with me,” say Ég er með bankakort (and for “the card,” Ég er með bankakortið).

How do I ask “Do you have a bank card?” in a natural way?

Two common options:

Ownership: Áttu bankakort? (colloquial contraction of Átt þú…?)
Having it on you: Ertu með bankakort?

How do I say “I don’t have a bank card”?

Ownership: Ég á ekki bankakort.
On me: Ég er ekki með bankakort. With the definite form: Ég á ekki bankakortið = I don’t have the bank card.

How do you pronounce the sentence?

Approximate guidance:

Ég: like “yeh” with a long vowel; the g is a soft fricative, not a hard g (IPA: [jɛːɣ]).
á: like “ow” in “cow” (IPA: [au]).
banka: the nk is like English “ngk” in “bank.”
kort: trilled r; o is short (like British “o” in “off”); final t is crisp. Overall: [jɛːɣ au ˈpaŋkaˌkʰɔr̥t] is a careful IPA rendering; don’t worry about being perfect—aim for “Yeh-ow BANG-ka-kort.”

What do the accent marks (é, á) tell me?

They’re separate letters with distinct sounds, not stress marks:

é ≈ [jɛ] (a y-sound plus open e)
á ≈ [au] (like “ow”) Stress in Icelandic normally falls on the first syllable of each word (and the first element of compounds), not where the accents are.

Why is it banka-kort and not banki-kort?

Compounds frequently use the genitive (or a linking form) of the first noun. Banki (a bank) has genitive singular banka, so bankakort literally “bank’s card” → “bank card.”

What gender is bankakort, and how does that affect other words?

Bankakort is neuter. Adjectives and pronouns agree in gender/number/case:

nýtt bankakort (a new bank card; neuter nominative/accusative singular)
bankakortið mitt (my bank card; neuter definite + neuter possessive)

How do I say “I had a bank card” or “I’ve had a bank card”?

Verb að eiga (to own) is irregular:

Present: ég á, þú átt, hann/hún/það á, við eigum, þið eigið, þeir/þær/þau eiga
Past: ég átti, þú áttir, hann átti, við áttum, þið áttuð, þeir áttu
Perfect: ég hef átt Examples:
Ég átti bankakort. (I had a bank card.)
Ég hef átt bankakort. (I’ve had a bank card.)

Is there a difference between bankakort, debetkort, and kreditkort?

Yes:

bankakort often refers to a bank-issued debit card in everyday speech.
debetkort explicitly means debit card.
kreditkort means credit card. You’ll also see the broad term greiðslukort (payment card). Context determines which is most natural.