Hún kom hlæjandi inn í stofuna og sagði að allt væri tilbúið.

Hlæjandi is the present participle of hlæja (to laugh). In this sentence, it means laughing and describes how she came in:

• Hún kom hlæjandi inn í stofuna = She came into the living room laughing

It functions a bit like an adverbial expression in English: it tells you what she was doing at the same time.

No. Hlæjandi is normally indeclinable, so it does not change for gender, number, or case.

So whether the subject is hann, hún, þau, etc., the form stays hlæjandi.

Inn í expresses movement into something:

• inn í stofuna = into the living room

This is different from a location phrase:

• í stofunni = in the living room / inside the living room

A useful contrast is:

• Hún fór inn í stofuna = She went into the living room
• Hún var í stofunni = She was in the living room

So here, because she is moving inward, inn í is used.

Because stofuna is the definite accusative singular form of stofa (living room, sitting room).

Here is the idea:

• stofa = a living room
• stofan = the living room (nominative)
• stofuna = the living room (accusative)

Since inn í with movement takes the accusative, we get inn í stofuna.

Here að means that and introduces a subordinate clause:

• sagði að allt væri tilbúið = said that everything was ready

This is very common after verbs of saying, thinking, knowing, etc.

For example:

• Hann sagði að hún kæmi. = He said that she was coming / would come.

Væri is the past subjunctive of vera (to be).

In reported speech after a past-tense verb like sagði, Icelandic often uses the subjunctive to show that this is the reported content of what someone said, rather than the speaker directly stating it as fact.

So:

• Hún sagði að allt væri tilbúið. = She said that everything was ready.

This is a very natural pattern in Icelandic indirect speech.

Sometimes you may see var, but væri is especially common in indirect/reported speech, particularly when the speaker is simply reporting what was said.

Very roughly:

• væri = reported statement, a little more detached
• var = can sound more like the speaker is also treating it as straightforward fact

For a learner, the safest takeaway is:

• after sagði að..., seeing the subjunctive like væri is completely normal

Because tilbúið agrees with allt, which is neuter singular.

• allt = everything
• tilbúið = ready in the neuter singular

So the grammar matches:

• allt væri tilbúið = everything was ready

Compare:

• hann var tilbúinn = he was ready
• hún var tilbúin = she was ready
• það var tilbúið = it was ready

Allt means everything here.

It comes from allur (all, whole) and is the neuter singular form. Icelandic often uses the neuter singular in this way for general ideas:

• allt = everything
• margt = much / many things
• ekkert = nothing

So allt væri tilbúið literally means everything would-be ready / was said to be ready.

Yes, it is very natural.

The structure is:

• Hún — subject
• kom — verb
• hlæjandi — participial description
• inn í stofuna — direction/place
• og sagði — second verb
• að allt væri tilbúið — subordinate clause

So the sentence flows as:

• She came in laughing and said that everything was ready

That is a very typical Icelandic way to build the sentence.

A fairly literal breakdown is:

• Hún = she
• kom = came
• hlæjandi = laughing
• inn í stofuna = into the living room
• og = and
• sagði = said
• að = that
• allt = everything
• væri = were / was (subjunctive, in reported speech)
• tilbúið = ready

So a close literal version would be:

• She came laughing into the living room and said that everything was ready.

A more natural English translation is:

• She came into the living room laughing and said that everything was ready.