Ég er ekki eins þreyttur og í gær.

Because in a normal Icelandic main clause, the finite verb usually comes early, and ekki normally follows it.

So the structure is:

• Ég = I
• er = am
• ekki = not

That gives Ég er ekki ... = I am not ...

This is very typical Icelandic word order.

Eins ... og is the pattern for as ... as.

So:

• eins þreyttur og ... = as tired as ...
• ekki eins þreyttur og ... = not as tired as ...

This is different from using a comparative adjective such as more tired.

Not really in the usual sense.

The word og is the same word that often means and, but in the expression eins ... og, it functions as part of a comparison:

• eins ... og = as ... as

So here og is not connecting two separate things the way and normally does in English. It is helping form the comparison.

Because Icelandic adjectives agree with the person or thing they describe.

Here the adjective is describing ég = I, and þreyttur is the masculine singular form. So this version would normally be said by a male speaker.

A female speaker would usually say:

• Ég er ekki eins þreytt og í gær.

So the adjective changes form depending on gender.

That is a very natural question. The full idea is basically:

• Ég er ekki eins þreyttur og ég var í gær.
• I am not as tired as I was yesterday.

In the shorter sentence, Icelandic leaves out the repeated part because it is understood from context:

• Ég er ekki eins þreyttur og í gær.

This kind of shortening is normal and natural.

Í gær means yesterday.

Even though English uses just one word, Icelandic uses this fixed expression with í. It is best learned as a complete chunk:

• í dag = today
• í gær = yesterday

So you should not try to translate it word-for-word too literally. Just remember í gær as the normal Icelandic way to say yesterday.

Because this sentence is built as an equality comparison, not a comparative.

• eins þreyttur og ... = as tired as ...
• ekki eins þreyttur og ... = not as tired as ...

If you used þreyttari, that would mean more tired:

• Ég er þreyttari en í gær. = I am more tired than yesterday.

So the sentence you have is specifically saying not as tired as yesterday, not more tired or less tired with a comparative adjective.

Yes, absolutely.

That version is more explicit because it includes the verb var = was:

• Ég er ekki eins þreyttur og ég var í gær.

The shorter version:

• Ég er ekki eins þreyttur og í gær.

is also natural, but it leaves out information that is already obvious.

So:

• shorter version = more compact, everyday, natural
• fuller version = clearer for learners, also fully correct

A rough guide:

• þ is like the th in thin
• æ is roughly like the vowel sound in eye

So:

• þreyttur starts with a th sound, not a t
• gær has a vowel roughly like eye

A very rough English-style approximation would be something like:

• THRAYT-tur for þreyttur
• gair/gye-r for gær

But the real Icelandic pronunciation is better learned by listening to native audio.