Á mánudögum drekk ég meira kaffi.

It means on Mondays in the sense of a habitual/repeated action.

Icelandic often uses the plural for this kind of meaning, just like English does in on Mondays, in the evenings, and so on. So:

• Á mánudögum = on Mondays / every Monday
• it does not mean one specific Monday

If you wanted a single Monday, you would normally use a singular form instead.

Mánudögum is the form used here in the common expression meaning on Mondays.

The noun mánudagur means Monday, and mánudögum is its dative plural form. With repeated weekday expressions like this, Icelandic commonly uses this form after á:

• á mánudögum = on Mondays
• á þriðjudögum = on Tuesdays
• á föstudögum = on Fridays

So this is a very useful pattern to learn as a whole.

Because Icelandic is usually a verb-second language.

That means the finite verb normally comes in the second position of a main clause. Here, the sentence starts with the time phrase Á mánudögum, so the verb comes next:

• Á mánudögum
  • drekk
    • ég
      • meira kaffi

So:

• Á mánudögum drekk ég meira kaffi. = natural Icelandic word order
• Ég drekk meira kaffi á mánudögum. = also possible, if you start with ég

Both are correct, but the structure changes depending on what comes first.

Drekk is the present tense, first person singular form of the verb drekka = to drink.

So:

• ég drekk = I drink
• þú drekkur = you drink
• hann/hún/það drekkur = he/she/it drinks

In this sentence, drekk means I drink.

Because meira is the correct comparative form here for more coffee.

The idea is that kaffi is a neuter singular noun, and in this kind of phrase the comparative word appears as meira:

• meira kaffi = more coffee

So the sentence is talking about a greater amount of coffee, not comparing two people in some adjective-like way.

A useful phrase to memorize is simply:

• meira kaffi = more coffee
• minna kaffi = less coffee

It actually fits the grammar of the sentence, but the form happens to look the same.

Kaffi is the direct object of drekka, and that object is normally in the accusative. But kaffi is a neuter noun, and in the singular its nominative and accusative forms are the same.

So even though the case is what you would expect for an object, the word still appears as:

• kaffi

This is very common with neuter nouns in Icelandic.

Because the sentence is talking about coffee in general, not a specific coffee.

This is very similar to English:

• I drink more coffee
  not usually
• I drink more the coffee

In Icelandic, mass nouns like kaffi often appear without the definite article when you mean the substance in general or an amount of it.

So:

• meira kaffi = more coffee

is the natural way to say it.

Yes. That is also correct.

Compare:

• Á mánudögum drekk ég meira kaffi.
• Ég drekk meira kaffi á mánudögum.

Both mean the same basic thing. The difference is mainly word order and what comes first in the sentence.

• Starting with Á mánudögum puts the time frame first: On Mondays...
• Starting with Ég puts the subject first: I drink...

Both are natural.

You would usually use a singular expression instead of á mánudögum.

Common possibilities are:

• á mánudag = on Monday
• á mánudaginn = on Monday / on the Monday / this Monday, depending on context

So the contrast is:

• á mánudögum = on Mondays, regularly
• á mánudag / á mánudaginn = on Monday, one occasion

That plural vs. singular difference is an important one in Icelandic time expressions.