Safnefnið er í góðu lagi.

The dictionary form is safnefni. In the sentence, it has the suffixed definite article, so safnefnið means the safnefni.

That is a very common Icelandic pattern: instead of putting a separate word for the before the noun, Icelandic usually attaches it to the end.

• safnefni = indefinite
• safnefnið = definite

Because this is a neuter singular noun of this type, the written result is -ið.

It is in the nominative singular because it is the subject of the sentence.

In Safnefnið er í góðu lagi, the thing being talked about is Safnefnið, so it takes the nominative case.

Also, with many neuter nouns, the nominative and accusative look the same, so the form itself does not always tell you the function by itself. Here, the sentence structure shows that it is the subject.

Because the subject is singular.

• er = is
• eru = are

Since Safnefnið refers to one thing, Icelandic uses er:

• Safnefnið er ... = The safnefni is ...

If the subject were plural, then you would use eru.

Literally, it is something like in good order, in good condition, or in a good state.

But as a whole expression, it usually means:

• okay
• fine
• all right

So this is a good example of an Icelandic phrase that is best learned as a unit, not word-by-word only.

Because the preposition í takes the dative here.

In this sentence, í does not mean motion into something. It describes a state/condition, so Icelandic uses the dative.

That gives you:

• lag → lagi (dative singular)
• góður → góðu (to agree with lagi)

So í góðu lagi is a dative phrase.

A useful general rule is:

• í + accusative often suggests movement into something
• í + dative often suggests location or state

Here it is clearly a state, so dative is used.

Yes. Lag has several meanings in Icelandic. In other contexts it can mean things like tune, melody, or shape/form.

But in í góðu lagi, it means something like:

• condition
• state
• order

So in this sentence, it does not mean song or melody.

Yes, very much so. It is a common Icelandic idiomatic expression.

Learners often do best by treating it as a chunk:

• í lagi = okay / all right
• í góðu lagi = fine / perfectly okay / in good shape

The version with góðu feels a bit fuller or more reassuring than just í lagi.

Yes. That would also be natural.

The difference is roughly this:

• í lagi = okay, all right
• í góðu lagi = fine, in good condition, perfectly okay

In many situations, both work. The version with góðu can sound slightly stronger, more positive, or more explicit.

Because er gott and er í góðu lagi are similar, but not identical.

• er gott = is good
• er í góðu lagi = is okay / is fine / is in good condition

So gott talks more directly about quality.
í góðu lagi often talks more about state, acceptability, or condition.

In English, compare:

• It is good
• It is fine
• It is okay
• It is in good shape

Those overlap, but they are not always exactly the same.

No. This is a very normal, neutral Icelandic sentence pattern:

• Safnefnið = subject
• er = verb
• í góðu lagi = complement / predicate phrase

So it is simply:

Subject + verb + phrase describing the subject

That is the most straightforward way to say it.

Icelandic can change word order for emphasis, but this version is the standard unmarked one.