Dýralæknirinn athugar örmerkið rétt áður en hann skráir örmerkjarnúmerið.

Those endings are the suffixed definite article in Icelandic. Instead of a separate word like the, Icelandic usually attaches the article to the noun.

• dýralæknirinn = the vet / the veterinarian
• örmerkið = the microchip
• örmerkjarnúmerið = the microchip number

Very roughly:

• masculine singular nominative often has -inn
• neuter singular nominative/accusative often has -ið

So these endings are doing the job that the does in English.

Icelandic normally does not use an indefinite article like English a/an.

So:

• dýralæknir = a vet / vet
• dýralæknirinn = the vet

Likewise:

• örmerki = a microchip / microchip
• örmerkið = the microchip

If you removed the article in this sentence, it would become less specific, more like A vet checks a microchip...

Hann means he, and it refers back to dýralæknirinn.

It is normal and expected here. Icelandic usually does not drop subject pronouns the way some languages do, so hann is needed in the subordinate clause.

This also shows that the sentence is referring to a male veterinarian, or at least using masculine reference.

They are the direct objects of the verbs:

• athugar örmerkið = checks the microchip
• skráir örmerkjarnúmerið = records the microchip number

These verbs take the accusative object.

In this sentence, both nouns are neuter singular, and for many neuter nouns the nominative and accusative look the same, so you do not see a separate ending change here. The role is shown by syntax and the verb, not by a visibly different form.

Here are the main base forms:

• dýralæknirinn → dýralæknir = veterinarian
• athugar → athuga = to check, examine
• örmerkið → örmerki = microchip
• rétt → rétt = right, just
• áður en = before
• hann = he
• skráir → skrá = to register, record
• örmerkjarnúmerið → örmerkjarnúmer = microchip number

Looking up the dictionary forms is often the easiest way to recognize what is going on grammatically.

Both are present tense, 3rd person singular:

• athugar = checks / is checking
• skráir = records / is recording

They agree with a singular subject:

• dýralæknirinn
• hann

This is a very normal use of the present tense in Icelandic, just like English can say The vet checks the microchip before he records the number.

Áður en means before.

Adding rétt makes it stronger and more precise:

• áður en = before
• rétt áður en = just before / right before

So rétt is acting like an intensifier here.

If you removed it, the sentence would still be correct, but the meaning would be a little less specific:

• áður en hann skráir... = before he records...
• rétt áður en hann skráir... = just before he records...

Here, en is part of the fixed expression áður en = before.

So it is best to learn áður en as a unit.

That means you should not read this en on its own as but. In this sentence, the whole phrase rétt áður en hann skráir... introduces the time relationship: just before he records...

Because this is a subordinate clause introduced by áður en.

In Icelandic, main clauses often follow the verb-second pattern, but subordinate clauses usually have more straightforward subject + verb order.

So this is normal:

• ... áður en hann skráir örmerkjarnúmerið

That is why you see hann skráir, not inversion.

Icelandic uses compound nouns very heavily.

Two good examples here are:

• dýralæknir = animal-doctor = veterinarian

  • dýra = of animals
  • læknir = doctor

• örmerkjarnúmer = microchip number

A useful rule: in Icelandic compounds, the last part usually determines the grammatical gender and inflection of the whole word.

So with örmerkjarnúmerið, the final element is númer, which is neuter, and that is why the whole compound behaves as a neuter noun and takes -ið in the definite singular.

Also, Icelandic compounds sometimes contain a linking element between parts, so the spelling is not always just a simple one-to-one joining of the basic words. Often you learn the standard compound as a whole word.

Yes.

• Dýralæknirinn athugar örmerkið áður en hann skráir örmerkjarnúmerið.

This still means The vet checks the microchip before he records the microchip number.

Adding rétt gives the sense of immediately/just before, so it adds a small nuance rather than changing the basic grammar.

Because Icelandic usually expresses the by attaching it to the end of the noun.

That is why you see:

• dýralæknirinn rather than a separate word before dýralæknir
• örmerkið rather than a separate word before örmerki
• örmerkjarnúmerið rather than a separate word before örmerkjarnúmer

This is one of the biggest structural differences from English, and it takes a little time to get used to.