Ég tala ekki mikið í dag, því ég er hás og þarf að hvíla mig.

Yes. A very literal breakdown is:

Ég = I
tala = speak
ekki = not
mikið = much / a lot
í dag = today
því = because
ég er hás = I am hoarse
og þarf að hvíla mig = and need to rest myself

So the sentence is built quite similarly to English, except that Icelandic says rest myself where English usually just says rest.

Because tala is the 1st person singular present form of að tala.

With this verb, the present tense goes like this:

• ég tala = I speak
• þú talar = you speak
• hann/hún/það talar = he/she/it speaks

So tala is the correct form with ég.

In a normal Icelandic main clause, ekki usually comes after the finite verb.

So:

• Ég tala ekki = I do not speak
• not Ég ekki tala

That is one of the most important word-order patterns to get used to in Icelandic.

Here mikið means much / a lot, and it is being used adverbially to describe how much speaking is happening.

So:

• tala mikið = speak a lot
• tala ekki mikið = not speak much

This is why you do not need a noun after it. It is not a lot of something; it is simply a lot in general.

You could also hear Ég tala lítið í dag, which means something very similar: I speak little / I’m not talking much today.

Í dag is a fixed and very common Icelandic expression meaning today.

Literally:

• í = in
• dag = day

But you should learn í dag as a whole expression, not by trying to translate it word-for-word every time. Icelandic often uses prepositional expressions for time in ways that do not match English exactly.

Yes. In this sentence, því means because / since.

So:

• ..., því ég er hás = ..., because I am hoarse

A longer alternative is af því að, which also means because:

• Ég tala ekki mikið í dag, af því að ég er hás...

Both are common. Því is shorter and very natural.

Hás is an adjective, and here it means hoarse.

It comes after er and describes the subject ég, so it works like a predicate adjective:

• ég er hás = I am hoarse

This is the same basic pattern as:

• ég er þreytt(ur) = I am tired
• ég er veik(ur) = I am sick

Because the subject is still understood to be the same person.

In:

því ég er hás og þarf að hvíla mig

the subject ég applies to both verbs:

• ég er hás
• [ég] þarf að hvíla mig

Icelandic, like English, often leaves out the repeated subject when two verbs are joined with og and the subject is the same.

It comes from the verb að þurfa = to need / have to.

The present singular form is þarf:

• ég þarf = I need
• hann/hún þarf = he/she needs

So this verb is not formed as simply as að tala → ég tala. It is an irregular and very common verb, so it is worth memorizing early.

There are two separate things happening here.

First, að: After þarf, Icelandic normally uses að + infinitive:

• ég þarf að fara = I need to go
• ég þarf að sofa = I need to sleep
• ég þarf að hvíla mig = I need to rest

Second, mig: The verb is commonly used as hvíla sig, literally rest oneself.

So:

• ég hvíli mig = I rest
• hann hvílir sig = he rests

Here mig is the accusative form of ég.

Very roughly, using English-style approximations:

• Ég ≈ yeg
• ekki ≈ EHK-ki
• mikið ≈ MEE-kith
• því ≈ thvee with th as in thing
• hás ≈ house
• þarf ≈ tharf with th as in thing
• hvíla ≈ KVEE-la

A few useful sound notes:

• þ is like th in thing
• á usually sounds like ow in cow
• hv is often pronounced close to kv

These are only rough guides, but they are good enough to get you started.