Ég rugla stundum nöfnum á mánudögum þegar ég sef illa.

Here rugla means to mix up / to confuse.

In this sentence, Ég rugla nöfnum means I mix up names.

A very common pattern is:

• rugla einhverju = to mix something up
• rugla einhverju saman = to mix things up with each other

So this sentence is using rugla in the sense of mentally confusing one name for another.

Because rugla here takes the thing being mixed up in the dative case.

• nominative/accusative plural: nöfn = names
• dative plural: nöfnum = names

So:

• Ég rugla nöfnum = I mix up names

This is something learners often just have to memorize with the verb: að rugla einhverju.

Because Icelandic often uses the plural for repeated events that happen on a certain day of the week.

• á mánudag = on a Monday / on Monday (one specific Monday, or sometimes more general in some contexts)
• á mánudögum = on Mondays

Since the sentence means this happens habitually, the plural makes sense:

• Ég rugla stundum nöfnum á mánudögum = I sometimes mix up names on Mondays

The ending -um shows the dative plural, because á often governs the dative when it means on in time expressions.

Stundum means sometimes.

It is an adverb of frequency, and its position is quite natural here:

• Ég rugla stundum nöfnum...

This is similar to English I sometimes mix up names...

You may also see adverbs move around in Icelandic depending on emphasis, but this placement is very normal and neutral.

Þegar means when.

It introduces a subordinate clause:

• þegar ég sef illa = when I sleep badly

So the whole sentence means that the speaker sometimes mixes up names on Mondays when they have slept badly.

Because sef is the 1st person singular present tense form of að sofa = to sleep.

This verb changes stem in the present tense:

• infinitive: sofa
• ég-form: sef
• þú-form: sefur
• hann/hún/það: sefur

So:

• ég sef = I sleep

This is an irregular change, so it is worth memorizing.

Illa is the adverb meaning badly / poorly.

Since it describes how the person sleeps, Icelandic uses an adverb, not an adjective:

• að sofa illa = to sleep badly

Compare:

• illur = bad, evil, sick (adjective form, used with nouns)
• illa = badly (adverb)

So ég sef illa means I sleep badly or I don’t sleep well.

Yes, that is a very close literal translation.

Word by word:

• Ég = I
• rugla = mix up
• stundum = sometimes
• nöfnum = names
• á mánudögum = on Mondays
• þegar = when
• ég sef illa = I sleep badly

A natural English rendering would be:

• I sometimes mix up names on Mondays when I sleep badly.

Depending on context, English might also say:

• I sometimes get names mixed up on Mondays when I haven’t slept well.

The most natural reading is that á mánudögum goes with the main clause:

• Ég rugla stundum nöfnum á mánudögum = I sometimes mix up names on Mondays
• þegar ég sef illa = when I sleep badly

So the sleep clause gives the condition or circumstance.

In real usage, context helps. Without extra punctuation or emphasis, the sentence most naturally means:

• On Mondays, if I’ve slept badly, I sometimes mix up names.

Great question. Icelandic is a V2 language in main clauses, meaning the finite verb often comes in the second position there. But after a subordinating conjunction like þegar, the clause is a subordinate clause, and the word order is different.

So you get:

• main clause: Ég rugla stundum nöfnum...
• subordinate clause: þegar ég sef illa

Not:

• þegar sef ég illa in this sentence

That would not be the normal subordinate-clause order.

Yes, but it changes the feel slightly.

• rugla nöfnum = mix up names
• rugla nöfnum saman = mix names up / confuse names with each other

Adding saman can make the idea of confusing things together more explicit.

So both are possible, but the sentence without saman is already perfectly natural.

Yes, mánudagur = Monday is a masculine noun.

Useful forms:

• nominative singular: mánudagur
• accusative singular: mánudag
• dative singular: mánudegi
• dative plural: mánudögum

In the sentence, you see:

• á mánudögum

That is the dative plural, used because the meaning is on Mondays.

Yes. A few possible alternatives are:

• Ég rugla stundum saman nöfnum á mánudögum þegar ég sef illa.
• Ég ruglast stundum á nöfnum á mánudögum þegar ég sef illa.

These are close in meaning, but the grammar shifts a little:

• Ég rugla nöfnum = I mix up names
• Ég ruglast á nöfnum = I get confused about names / I mix up names

The original sentence is completely natural, but Icelandic often allows more than one way to express the same idea.