Ég sendi ritgerðina ekki fyrr en ég hef athugað hverja heimild vandlega.

Formally, sendi can be either:

• present tense, 1st person singular: ég sendi = I send / I am sending
• past tense, 1st person singular: ég sendi = I sent

So yes, the form is ambiguous on its own.

In this sentence, it is understood as present with future meaning: I won’t send the essay until... Icelandic often uses the present tense where English would use will. The context makes the future reading clear.

Icelandic has no separate future tense ending like English will send. Very often, Icelandic simply uses the present tense for future actions when the meaning is clear from context.

So:

• Ég sendi ritgerðina ekki fyrr en...
  naturally means I won’t send the essay until...

You can use munu to make the future more explicit, but that is not necessary here and would usually sound less neutral.

Ekki fyrr en is a very common expression meaning not until.

So:

• ekki fyrr en ég hef athugað... = not until I have checked...

Literally, it is something like not earlier than when, but you should learn it as a set phrase:

• ekki fyrr en = not until

Because ritgerðina is the direct object of sendi.

The noun is:

• ritgerð = essay
• feminine noun

Here it is:

• singular
• definite = the essay
• accusative, because it is the object of senda

So:

• ritgerð = essay
• ritgerðin = the essay (nominative)
• ritgerðina = the essay (accusative)

Hef athugað is the present perfect:

• hef = have
• athugað = past participle of athuga

This shows that the checking must be completed before the sending happens.

So the idea is:

• first: I check every source carefully
• then: I send the essay

That is why I have checked fits well here, just like in English after until.

Because this is a subordinate clause.

In Icelandic main clauses, the finite verb often comes in second position (V2 word order). But in subordinate clauses, the word order is usually more straightforward:

• subject + finite verb + rest

So after en here, you get:

• ég hef athugað...

not:

• hef ég athugað...

That is a very common pattern in Icelandic subordinate clauses.

Because athuga takes a direct object, and here that object is in the accusative singular.

The noun is:

• heimild = source, feminine

The word hverja has to agree with heimild in:

• gender: feminine
• number: singular
• case: accusative

So:

• hverja heimild = each/every source

Yes. Hver can mean different things depending on context.

It can mean:

• who
• which
• each / every

In hverja heimild, it has the distributive sense each/every.

So the sentence means checking sources one by one, not asking which source?

That usage is very common in Icelandic.

Vandlega is an adverb meaning carefully or thoroughly.

It modifies athugað:

• athuga vandlega = check carefully

Its position at the end is natural and idiomatic here. Icelandic adverb placement is somewhat flexible, but putting vandlega after hverja heimild sounds very normal:

• athugað hverja heimild vandlega

The final position gives a smooth, natural emphasis to how the checking is done.