Learn Hardcore Icelandic: Við gerum áætlun saman.

Yes. Icelandic simple present often covers English simple and progressive aspects. Við gerum áætlun saman can mean either We make a plan together (habitual/general) or We are making a plan together (right now). If you want to emphasize in-progress action, you can also say Við erum að gera áætlun (saman).

Why is there no word for a before plan?

Icelandic has no indefinite article. A bare noun often corresponds to English with a/an. So áætlun here means a plan. The definite article is a suffix: áætlunin = the plan.

What does each word mean and what part of speech is it?

Við: pronoun, nominative plural = we.
gerum: verb, present tense 1st person plural of gera = do/make.
áætlun: noun (feminine) = plan/schedule.
saman: adverb = together.

What verb is gerum from, and how is it conjugated?

It’s from gera (to do/make).

Present: ég geri, þú gerir, hann/hún/það gerir, við gerum, þið gerið, þeir/þær/þau gera
Past: ég gerði, þú gerðir, hann/hún/það gerði, við gerðum, þið gerðuð, þeir/þær/þau gerðu
Past participle: gerður (m), gerð (f), gert (n)
Imperative: gerðu! (sg), gerið! (pl); 1st pl hortative: Gerum!

What case is áætlun in, and how does it decline?

It’s the direct object, so accusative singular. For this noun, nominative and accusative singular look the same.

Singular: Nom áætlun, Acc áætlun, Dat áætlun, Gen áætlunar
Plural: Nom áætlanir, Acc áætlanir, Dat áætlunum, Gen áætlana Definite forms (examples): áætlunin (Nom sg), áætlunina (Acc sg).

Why is saman at the end? Can it go elsewhere?

Adverbs like saman often come after the object, so Við gerum áætlun saman is very natural. You can also say:

Við gerum saman áætlun (also common)
Saman gerum við áætlun (emphasizes togetherness) Keep the finite verb in 2nd position in main clauses (V2): Saman gerum við …, not Saman við gerum ….

Is við here the same word as the preposition við (with/against/by)?

No. Here Við is the pronoun we. There is also a preposition við (governs accusative) meaning things like by/against/with depending on context. They’re homographs but different parts of speech.

How do I pronounce the sentence?

Approximate guide:

Við: like English v + the th in this; roughly “vith” (the vowel is like short i but can be long here).
gerum: roughly “GEH-rum” (g is palatal before e; r is trilled; u like German ü).
áætlun: roughly “OW-eye-tlun” (á like ow in now; æ like eye; tl cluster is crisp; u like ü; final n).
saman: roughly “SAH-man” (first syllable stressed). Stress each word on the first syllable.

Could I say Við gerum planið saman to mean We make the plan together?

Yes, if you mean a specific, known plan: planið is the definite form of the loanword plan (neuter). More idiomatic/formal is to use áætlun: Við gerum áætlunina saman.

Is gera áætlun the normal way to say make a plan?

Yes. Common collocations include:

gera áætlun (make/draw up a plan)
setja upp áætlun (set up a plan)
búa til áætlun (create a plan; fine, slightly more literal) Note: áætlun can also mean schedule; e.g., tímaáætlun = timetable.

What’s the difference between gera áætlun and ætla (to intend/plan to)?

gera áætlun = to create a plan (a document/outline).
ætla (að) = to intend/be going to. Example: Við ætlum að gera áætlun = We intend to make a plan / We’re going to make a plan. Don’t say gera áætlun að … to mean intend to do something.

How would I say We don’t make a plan together?

Við gerum ekki áætlun saman. Place ekki after the finite verb.

Can Icelandic drop the subject pronoun like Spanish/Italian?

Generally no. Icelandic is not a pro-drop language. You normally need the subject pronoun, so Við gerum …, not just Gerum …, unless you’re using the imperative/hortative Gerum …! (Let’s …).

How do I say with him together, as in We make a plan together with him?

Use með plus dative for with:

Við gerum áætlun með honum. You can add saman for emphasis: Við gerum áætlun með honum, saman. Usually með honum already implies togetherness.

What are the plural forms for plan?

áætlun (sg) → áætlanir (pl): Við gerum nokkrar áætlanir = We make several plans.
The loanword plan (n.) has plural plön: Við gerum plön (colloquial). áætlun/áætlanir is preferred in formal contexts.

Why is the verb in second position? Could I front another element?

Main clauses in Icelandic are V2 (verb-second). In Við gerum áætlun saman, the verb gerum is 2nd. If you front another element, the verb stays 2nd:

Saman gerum við áætlun.
Áætlun gerum við saman. This changes emphasis but is grammatically normal.

How would I make it specific, like We draw up the plan together?

Use the definite object:

Við gerum áætlunina saman. That means the plan (a particular one already known in context).