Learn Hardcore Icelandic: Matur inniheldur vatn.

Icelandic has no indefinite article a. Nouns without a suffixed ending are both generic and indefinite. To say the food, you attach the definite suffix -inn, yielding maturinn.

What case is vatn in here? It looks identical to the nominative.

It’s the direct object, so it’s in the accusative case. For many neuter nouns like vatn, the nominative and accusative indefinite forms coincide.

What does the prefix inni- add to halda, and where does inniheldur come from?

The base verb halda means to hold. Adding the prefix inni- (in/inside) gives innihalda, to hold inside → to contain. inniheldur is the present 3rd-person form of að innihalda.

What tense and person is inniheldur, and how is að innihalda conjugated in the present?

inniheldur is present tense, 3rd person singular. The full present-tense conjugation of að innihalda is:
• ég inniheld (1st sg.)
• þú inniheldur (2nd sg.)
• hann/hún/það inniheldur (3rd sg.)
• við inniheldum (1st pl.)
• þið innihaldið (2nd pl.)
• þeir/þær/þau innihalda (3rd pl.)

What would Matur inniheldur vatnið mean?

With the suffix -ið, vatnið is definite (the water). So Matur inniheldur vatnið translates to The food contains the water, referring to specific water.

Why is the object vatn placed after inniheldur? How does Icelandic word order work?

Icelandic is a V2 language: the finite verb must occupy the second position in main clauses. Here:
1st slot: subject Matur
2nd slot: finite verb inniheldur
3rd slot onward: object vatn

Can matur be plural? How would you say foods in Icelandic?

The regular plural of matur is matar (nominative pl.), but that form is rare. For foods in the sense of food items, Icelandic typically uses matvæli, an indeclinable neuter plural.