Ég rugla þeim stundum saman.

A word-by-word breakdown is:

• Ég = I
• rugla = confuse / mix up
• þeim = them in the dative plural
• stundum = sometimes
• saman = literally together, but here it is part of the expression rugla saman, meaning mix up / confuse with each other

So the sentence structure is basically I confuse them sometimes together, but in natural English that becomes I sometimes mix them up or I sometimes confuse them with each other.

Here rugla is the present tense, meaning I confuse / I mix up.

This can be confusing because for many Icelandic verbs, the 1st person singular present has the same form as the infinitive. So:

• að rugla = to confuse / to mix up
• ég rugla = I confuse / I mix up

The subject Ég tells you that this is a full sentence in the present tense, not just an infinitive.

Because þeim is the dative plural form of they/them in Icelandic, and the expression rugla saman normally takes the thing or person being mixed up in the dative.

So although English just says them, Icelandic has to choose the correct case form, and here that form is þeim.

A very important point: þeim is used for all genders in the plural in the dative:

• masculine plural → þeim
• feminine plural → þeim
• neuter plural → þeim

Because those are different case forms.

• þá = masculine plural accusative
• þær = feminine plural nominative/accusative
• þau = neuter plural nominative/accusative

But in rugla þeim saman, the pronoun has to be in the dative plural, so the correct form is þeim.

This is one of the big differences between English and Icelandic: English just has them, but Icelandic changes the form depending on grammatical case.

As a set expression, rugla saman means to mix up, to confuse, or to fail to distinguish one thing/person from another.

So:

• Ég rugla þeim saman = I mix them up
• Ég rugla þeim stundum saman = I sometimes mix them up

The word saman is important here. By itself, rugla can have a broader sense like confuse or mess up, but rugla saman specifically gives the idea of mixing things up with each other.

Yes, exactly.

That with each other idea is built into rugla þeim saman. It means you do not properly keep them apart in your mind.

If you want to name what someone is confused with, Icelandic often uses við:

• Ég rugla honum saman við bróður hans.
  I confuse him with his brother.

So in your sentence, the other side of the comparison is not stated, because it is already understood: the members of the group are being mixed up with one another.

Stundum means sometimes.

Historically, it comes from a case form of the noun stund meaning time / moment / while, but as a learner, the most useful thing is to treat stundum as a fixed adverb meaning sometimes.

So you do not need to actively analyze it every time. Just learn:

• stundum = sometimes

This is a natural Icelandic main-clause order:

• Ég = subject
• rugla = finite verb
• þeim = object
• stundum = adverb
• saman = particle/adverb belonging closely with rugla

Icelandic word order is somewhat flexible, but this version sounds natural and neutral.

You can also move stundum for a different rhythm or emphasis, for example:

• Stundum rugla ég þeim saman. = Sometimes I mix them up.

That is also very natural. In your sentence, stundum sits in the middle, which is common.

Yes.

In this sentence, þeim can refer to:

• people
• animals
• objects
• ideas
• words
• names
• anything plural, as long as the grammar requires the dative plural

So Ég rugla þeim stundum saman could mean:

• I sometimes mix them up about two people
• I sometimes mix them up about two words
• I sometimes mix them up about several objects

The sentence itself does not tell you what them refers to; that comes from context.

Yes, literally saman means together, but in this sentence it should be understood idiomatically.

In rugla saman, it does not simply mean that the things are physically together. Instead, it contributes the sense of blending them in your mind or not keeping them separate.

So a literal translation is not very helpful here. It is better to learn the whole pattern:

• rugla e-u saman = mix something up
• rugla e-m saman við e-n = confuse someone with someone

The most natural translations are:

• I sometimes mix them up.
• I sometimes confuse them.
• I sometimes confuse them with each other.

The best choice depends on context, but I sometimes mix them up is often the most idiomatic everyday English equivalent.