Learn Hardcore Icelandic: Ég kaupi ekkert í dag, nema mjólk.

Ekkert is a pronoun meaning "nothing" and serves as the direct object of kaupi. Ekki is the adverb "not" and can’t be the object. If you use ekki, you pair it with neitt ("anything"): ekki neitt = "nothing."

Is ekkert the same as ekki neitt? Any difference in tone?

They both express "nothing" as an object: Ég kaupi ekkert í dag ≈ Ég kaupi ekki neitt í dag. Many speakers feel ekki neitt can be a little more colloquial/emphatic, but both are common and correct.

What case is mjólk in after nema? Does nema assign case?

Nema is a conjunction ("except/unless"), not a preposition, so it doesn’t assign case. The phrase after nema takes the case required by its role in the main clause. Here it stands for the direct object, so accusative. For mjólk, the form looks the same, but the underlying case here is accusative.

Why is there no article with mjólk? When would mjólkina be used?

Mjólk is a mass noun and is usually bare when you mean "some milk" in general. Use the definite form when you mean specific, known milk:

Ég kaupi ekki mjólkina í dag. = I’m not buying the milk today (the specific milk we know about). In your sentence, nema mjólk means "except (some) milk" in general.

Is the comma before nema necessary?

No; it’s stylistic. Both are fine:

Ég kaupi ekkert í dag, nema mjólk.
Ég kaupi ekkert í dag nema mjólk. The comma can reflect a spoken pause before the exception.

Where can í dag go? Are other word orders possible?

Yes. Icelandic is verb-second, but adverbials can move:

Neutral: Ég kaupi ekkert í dag.
Fronted time: Í dag kaupi ég ekkert.
With the exception: Í dag kaupi ég ekkert, nema mjólk. Placing í dag between verb and object (e.g., Ég kaupi í dag ekkert) is possible but sounds marked/awkward.

Could I say Ég kaupi bara mjólk í dag instead? What’s the difference from using nema?

Yes. Bara means "only": Ég kaupi bara mjólk í dag = "I’m only buying milk today." Your original …ekkert…, nema mjólk frames it as "nothing … except milk." The meanings are very close; bara is simpler and very common, while nema explicitly sets an exception to a negated statement.

Does nema ever mean "unless"?

Yes. With a finite clause, nema means "unless":

Ég kaupi það ekki, nema þú borgir. = I won’t buy it unless you pay. With a noun phrase, it means "except (for)": nema mjólk.

What’s the relationship between enginn/engin/ekkert and neitt?

enginn/engin/ekkert = "no/none" (determiner/pronoun). Neuter ekkert often stands alone as "nothing": Ég veit ekkert.
neitt = "anything" (negative-polarity). With ekki: ekki neitt = "nothing." You can also use engin with a noun: ég kaupi enga mjólk í dag = "I’m buying no milk today."

Why is the subject ég present? Can Icelandic drop subject pronouns?

No, not in standard usage. Icelandic isn’t a pro‑drop language, so you keep the subject: Ég kaupi…, not just Kaupi… (except imperatives or very special contexts).

Can I change the tense? How would past or future look?

Past: Ég keypti ekkert í dag, nema mjólk. (said later in the day)
Future: Ég mun ekki kaupa neitt í dag, nema mjólk.
You can also say Ég mun kaupa ekkert í dag, nema mjólk, though many prefer pairing mun with ekki neitt.

How do I negate only "milk" (I’m not buying milk today) rather than everything?

Negate the object:

Ég kaupi ekki mjólk í dag. = I’m not buying milk today (but I might buy other things).
Ég kaupi ekkert í dag. = I’m buying nothing today.

Any quick pronunciation tips for Ég, kaupi, ekkert, mjólk?

Ég: starts with a y‑sound; final g is a soft fricative: roughly "yegh."
kaupi: kau like the ow in "cow": "KOW‑pi."
ekkert: strong kk; tapped r; voiceless t: roughly "EHK‑ert."
mjólk: m + y‑glide; long ó like "yo": roughly "MYO‑lk." These are approximations; Icelandic sounds differ from English.

Why is it í dag ("in day") for "today"? Any similar time expressions?

It’s a fixed idiom. Learn these as chunks:

í dag = today
í gær = yesterday
á morgun = tomorrow
í morgun = this morning (earlier today)

Can I also say Ég kaupi ekkert annað í dag en mjólk?

Yes. …ekkert annað… en… ("nothing else than…") is another natural way to express the same idea:

Ég kaupi ekkert annað í dag en mjólk. It’s slightly more explicit about "else," but the meaning matches "nothing today except milk."