I was dead and cold, now living and warm;
From one world, now of another;
Once one of many, now all alone;
Once a branch, then a seed.
Who am I?

takes a wild guess*

Is it Digs and Polly traveling with their rings?!

No, but you’re in the right book! Hint: it’s not a person.

Is it a lamppost?

Close enough! I was going for the bar.

Dark clouds and horrid smells abound
Whenever I am to be found.
I feed on the blood of men
Hates everything Narnian.
I stretch out my claws,
Open wide my jaws,
In the effort of snatching everything I see.
I can make you sick at the sight of me.

Who am I?

Tash "the inexorable, the irresistible!"

Yep 🙂

A upper class Calormene Captain
Who professes the name of Tash with word of mouth
Though doesn't really believe in Tash or any of the supernatural
Tash appears right before me in the stable

Rishda?!

Correct!

It's part of Jadis, but not of witch.
It's in the harness, but not the hitch.
Queen Susan has one, but Lu does not.
It's not in Tumnus' cooking pot.
What is it?

The letter A?

yes 🙂

I had travelled far and wide
Until the one who bore me died.
Collected dust, but never rust —
Memory dear kept oh so near.
Then a journey like none before,
To freedom and the North.