Það er ólíklegt að ég gleymi lyklunum aftur, því ég setti þá á sama stað og alltaf.

Það er works much like English it is in sentences such as It is unlikely that...
Here, það is a dummy subject: it does not really refer to a thing. The real content comes in the clause after it:

• Það er ólíklegt = It is unlikely
• að ég gleymi lyklunum aftur = that I will forget the keys again

So það here is grammatical structure, not a meaningful “that/it” referring to something specific.

Because the adjective is describing the whole situation/clause, not a specific masculine or feminine noun.

In Icelandic, when an adjective is used with an impersonal structure like Það er ... að..., it is often put in the neuter singular:

• ólíklegt = unlikely

So:

• Það er ólíklegt að... = It is unlikely that...

The neuter singular is the default form here.

Here að is a subordinating conjunction meaning that.

It introduces the clause:

• að ég gleymi lyklunum aftur = that I forget / will forget the keys again

English often drops that:

• It’s unlikely I’ll forget the keys again

But Icelandic usually keeps að in this kind of sentence.

After expressions like Það er ólíklegt að... (“It is unlikely that...”), Icelandic commonly uses the subjunctive because the speaker is talking about something uncertain, hypothetical, or judged as unlikely.

So gleymi is the expected form here.

A useful detail: in 1st person singular present, the form of the subjunctive often looks the same as the indicative, so you may not see a visible difference in the spelling. But grammatically, this kind of clause normally calls for the subjunctive.

Because Icelandic often uses the present tense for future meaning, especially when the future is clear from context.

So:

• að ég gleymi lyklunum aftur
  can naturally mean
• that I will forget the keys again

English often prefers will here, but Icelandic does not need a separate future tense form.

Because the verb gleyma (“to forget”) takes the dative case in Icelandic.

So the object is not in the accusative as an English speaker might expect. Instead:

• lyklunum = the keys in dative plural definite

Compare:

• lyklar = keys (nom.)
• lykla = keys (acc./gen. depending on context)
• lyklum = keys (dat. indefinite)
• lyklunum = the keys (dat. definite)

So gleyma lyklunum means forget the keys.

Because pronouns take the case required by their own role in the new clause, not the case of the noun they refer back to.

In the first clause:

• lyklunum is dative because gleyma takes dative

In the second clause:

• þá refers to the same keys, but now it is the direct object of setti (“put”), and setja takes an accusative object

So:

• lyklunum = dative plural
• þá = accusative plural masculine

The important point is that the reference stays the same, but the case changes because the grammar of the new clause is different.

Here því means because or since.

It introduces the reason:

• því ég setti þá á sama stað og alltaf
  = because I put them in the same place as always

This is a very common way to introduce a reason clause. You may also see af því að with a similar meaning, but því is shorter and very common in written and spoken Icelandic.

Setti is the past tense of setja (“to put, place”).

So:

• ég setti þá = I put them

The speaker is referring to an action already completed before the moment of speaking: they already put the keys somewhere.

Depending on context, English might say either:

• I put them
• I’ve put them

But Icelandic simply uses the past tense setti here.

With the preposition á, Icelandic usually distinguishes between:

• accusative for movement/destination
• dative for location

Because setja involves putting something to/onto a place, the phrase is understood as a destination, so grammatically accusative is expected here.

So in:

• ég setti þá á sama stað

the phrase after á is best understood as accusative.

A tricky point: with staður, the singular accusative and dative forms are both stað, so you cannot see the case difference in the spelling here. The adjective sama also looks the same in these forms, so the case is hidden on the surface.

The word for same is samur, but in actual use it usually appears in a weak form when it means the same:

• sami
• sama
• etc.

So:

• á sama stað = in/on/to the same place

This is the normal Icelandic pattern. You do not use the basic dictionary form samur here.

Also, sama already gives the noun a definite-like meaning, so you do not need an extra definite article.

Because after sami/sama (“same”), Icelandic uses og in the sense of as:

• sama stað og alltaf = the same place as always

So although og often means and, here it is part of a comparison-like structure.

You can think of it as:

• sama X og Y = the same X as Y

That is why á sama stað og alltaf means in the same place as always, not in the same place and always.

Yes, in a useful way.

The sentence has:

1. a main clause:
   Það er ólíklegt
2. an að-clause:
   að ég gleymi lyklunum aftur
3. a reason clause with því:
   því ég setti þá á sama stað og alltaf

Notice that in the subordinate clauses, Icelandic does not use the main-clause V2 pattern the same way it does in independent statements. So:

• að ég gleymi...
• því ég setti...

are normal subordinate-clause word orders.

That is one reason Icelandic sentences can look a bit different from main-clause patterns learners first study.