Yes!

Okay, I'm gonna try to make this one easier.

You might call me miserly,
but, really, can you blame me?
For in my days of hair so hoary,
I've been cursed with a life of poverty.

Gumpas? Arsheesh?

Arsheesh is correct. 🙂

Okay...

Strong magic upon me,
The king called me “son”,
Through an odd-looking portal
I was the first one.

King Frank?

Nope. Although that was a good guess.
Hint: this character is not named in the book.

OH! It's the first Telmarine to go through the Door in the Air!

Yes! Sorry it took me so long to get back. 😳

🙂
This one's probably going to be easy....

I too passed through a door,
I too was called "son",
but I couldn't stay long
'cause I was instructed to run.
Who am I?

Shasta/Cor?

Correct. 🙂

My weapon is always with me,
I have lived two lives,
With my best friend I love to be
In front of another I felt rather shy
Who am I?

Jewel?

Yep! 😀