Í janúar, þegar myrkrið er mest, reyni ég að halda áfram að læra á hverjum degi.

Í janúar means in January.

The preposition í is commonly used for being in a month, season, or other period of time. So this is the normal way to say in January in Icelandic.

A useful thing to remember is that month names often look unchanged in these expressions, so janúar stays janúar here.

Þegar means when.

It introduces a subordinate clause:

þegar myrkrið er mest = when the darkness is greatest / when it is darkest

So the sentence structure is basically:

• Í janúar = time setting
• þegar myrkrið er mest = a when-clause giving more detail
• reyni ég... = the main clause

Myrkrið is the definite form of myrkur, so it means the darkness.

Icelandic often uses the definite form when talking about something understood in the situation or something treated as a general phenomenon. Here it refers to the winter darkness in January, so the darkness sounds natural.

• myrkur = darkness
• myrkrið = the darkness

Here mest means greatest / most.

So myrkrið er mest is literally something like the darkness is greatest. In more natural English, that becomes when it is darkest or when the darkness is at its greatest.

This is a very Icelandic way of expressing the idea. Instead of focusing on it is dark, the sentence focuses on the darkness as a noun.

Mest is the superlative form related to mikill (great, much).

In this sentence, it agrees with myrkrið, which is neuter singular, so mest is the matching form.

You do not need to overthink this too much at first; the key point is:

• mest = most / greatest
• myrkrið er mest = the darkness is greatest

This is because of the Icelandic V2 rule: in a main clause, the finite verb usually comes in the second position.

Here, the sentence begins with a fronted time element:

Í janúar, þegar myrkrið er mest, ...

After that opening material, the finite verb comes next:

reyni

and then the subject:

ég

So:

• Ég reyni að læra... = neutral word order
• Í janúar ... reyni ég að læra... = verb comes before the subject because something else came first

This is one of the most important word-order patterns in Icelandic.

Reyni is the 1st person singular present form of reyna, meaning try.

So:

• ég reyni = I try

In this sentence, because of word order, it appears as:

• reyni ég = still I try

The meaning does not change; only the order changes.

Because two different verb relationships are involved.

First:

• reyna að + infinitive = try to + verb

So:

• reyni að halda áfram = I try to continue

Second:

• halda áfram að + infinitive = continue to + verb

So:

• halda áfram að læra = continue to learn

Put together:

• reyni að halda áfram að læra = I try to continue learning

So the two aðs are not accidental repetition; each one has its own job.

Yes. Halda áfram is a very common expression meaning continue, keep going, or carry on.

In this sentence:

• halda áfram að læra = continue learning / continue to learn

It helps to learn it as a unit:

• halda áfram = continue
• halda áfram að gera eitthvað = continue to do something

So áfram belongs with halda, not with læra.

Á hverjum degi means every day or more literally on each day.

This is a very common Icelandic expression.

A few useful details:

• hverjum is from hver = each / every
• degi is the dative form of dagur = day

So literally:

• á = on
• hverjum degi = each day

Together:

• á hverjum degi = every day

Because Icelandic often uses the singular with hver when the meaning is distributive: each day, every day.

So even though English speakers may think in terms of repeated days, Icelandic expresses it as on each day:

• á hverjum degi

This is completely normal and idiomatic.

Because þegar myrkrið er mest is an inserted subordinate clause.

The commas show that it is extra information placed inside the sentence after Í janúar and before the main clause reyni ég...

So the punctuation helps the reader see the structure:

• Í janúar = time phrase
• þegar myrkrið er mest = inserted when-clause
• reyni ég að halda áfram... = main clause

Without that middle clause, the simpler sentence would be:

Í janúar reyni ég að halda áfram að læra á hverjum degi.