Learn Hardcore Icelandic: Ég elska Ísland.

Ég ≈ “yegh” (one syllable; start with a y sound as in yes, then e as in bed, and finish with a soft g in the throat)
elska ≈ “EHL-ska” (stress on the first syllable)
Ísland ≈ “EES-land” (long ee sound at the start; stress on ÍS‑)

In IPA (more precise):

Ég = [jɛːɣ]
elska = [ˈɛlska]
Ísland = [ˈiːsland]

Stress is on the first syllable of elska and Ísland, and Ég is itself stressed because it’s a one‑syllable word.

Why is it Ég elska and not Ég elskar?

Because elska is correctly conjugated for I (Ég) in the present tense.

The present tense forms of að elska (to love) are:

Ég elska = I love
Þú elskar = You (singular) love
Hann / Hún / Það elskar = He / She / It loves
Við elskum = We love
Þið elskið = You (plural) love
Þeir / Þær / Þau elska = They love

So with Ég, the correct verb form is elska, not elskar.

Is elska here the infinitive, since it looks like the dictionary form?

No, in this sentence it is a conjugated verb form, not an infinitive.

The infinitive is að elska (to love). The word að is like the to in English.
When you actually use the verb with a subject, you drop að and conjugate the verb:
- Ég elska (I love)

The bare form elska happens to look the same in the infinitive (að elska) and in the 1st person singular present (ég elska), but its function in the sentence is different.

What grammatical case is Ísland in here, and what gender is it?

Ísland is:

Gender: neuter
Case in this sentence: accusative singular (because it is the direct object of the verb elska)

For many neuter nouns in Icelandic, the nominative and accusative singular forms are identical. Ísland is one of these.

Basic singular forms of Ísland:

Nominative: Ísland
Accusative: Ísland
Dative: Íslandi
Genitive: Íslands

So in Ég elska Ísland, Ísland is grammatically accusative, even though it looks the same as the nominative form.

Why don’t we say Ég elska Íslandið with a definite article, like I love the Iceland?

Two main reasons:

Country names normally do not take the definite article in Icelandic, just as in English we normally say I love Iceland, not I love the Iceland.
In Icelandic, the definite article is usually attached to the end of the noun. For neuter nouns like Ísland, the definite form is:
- Íslandið = the island / the Iceland (as a particular island)
That is typically used when talking about the landmass as a specific island, less so as the country in a general, abstract way.

So for the usual meaning (loving the country of Iceland), native speakers say Ég elska Ísland, without the definite article.

Why are Ég and Ísland capitalized, but elska is not?

Capitalization rules here:

Ísland is a proper noun (a country name), so it is always capitalized.
elska is a verb, so it is written with a lowercase letter, unless it starts a sentence (which it doesn’t here).
Ég is capitalized in this sentence because it is at the beginning of the sentence.
Unlike English I, the pronoun ég is not always capitalized in the middle of a sentence. Example:
- Ísland er fallegt og ég elska það.
  (Iceland is beautiful and I love it.)
  Here ég is lowercase.

So: first word of the sentence = capitalized, proper names = capitalized, regular verbs/pronouns otherwise start with lowercase.

Is the word order in Ég elska Ísland always subject–verb–object in Icelandic?

In this simple statement, Icelandic uses the same basic order as English:

Subject – Verb – Object
Ég (subject) elska (verb) Ísland (object)

However, Icelandic has a verb‑second (V2) rule in main clauses: the finite verb usually comes second, but different elements can come first. For example:

Ég elska Ísland. = I love Iceland.
Ísland elska ég. = Iceland, I love. (emphasis on Ísland)

In both cases, the verb is in second position in the clause. So S–V–O is the default, but word order is somewhat flexible because of the V2 rule.

Are there any nuance or politeness issues with using elska about a country?

Using elska for a country is normal and natural:

Ég elska Ísland. = I (really) love Iceland.

A few nuance points:

elska expresses fairly strong emotion, just like love in English.
For people, Ég elska þig is often quite intimate/romantic, though it can also be used for family.
For countries, cities, foods, etc., elska can be used quite freely, especially in emotional or enthusiastic contexts.

There is also a softer expression:

Mér þykir vænt um Ísland. = I am fond of Iceland / I care about Iceland.

But for a simple, enthusiastic statement, Ég elska Ísland is perfectly fine.

How would I change this sentence to say you, we, or they love Iceland?

Just change the subject pronoun and the verb form:

Þú elskar Ísland. = You (singular) love Iceland.
Við elskum Ísland. = We love Iceland.
Þið elskið Ísland. = You (plural) love Iceland.
Þeir elska Ísland. = They (masculine) love Iceland.
Þær elska Ísland. = They (feminine) love Iceland.
Þau elska Ísland. = They (neuter / mixed group) love Iceland.

The noun Ísland stays the same; only the pronoun and verb ending change.

What do the accented vowels É and Í mean here? Are they just stress marks?

They are not stress marks; they are distinct vowel letters that show sound quality (and often length), not word stress.

É / é in Ég represents a long vowel pronounced roughly like yeh (IPA [jɛː]).
Í / í in Ísland is a long ee‑type sound (IPA [iː]).

In Icelandic, stress is almost always on the first syllable of a word anyway, so you don’t need special stress marks. The acute accent changes how the vowel sounds, not where the stress goes.