The King James is a PROTESTANT Bible

TR:That is a poor translation because it left out the definite article that IS in the Greek.

The King James is a PROTESTANT Bible. 

Can such faith save him?
Can that kind of faith save anyone?
Can that faith save him?
This kind of faith cannot save him, can it?

That is precisely what that Protestant Bible is asking.

We all agree that faith (which is dead) can NOT save anyone.

Good. You just called it faith.

A faith that is dead has the same spiritual results as no faith

Correct. And, Catholic Teaching.

A faith that is dead has the same spiritual results as faithlessness.

Still correct. And Catholic Teaching.

once again,
you (and other Catholics) place "faith which is dead" in the same category as having a faith.

Just as you did when YOU said, We all agree that faith (which is dead) can NOT save anyone. You can't deny it because its quoted right above. 

I (and other protestants) place "faith which is dead" in the same category as having no faith.

Same as Catholics.

Also try a little more focus on the word "legó" which means to "say" or "claim".
"though a man say he hath faith"
In context, is the claim true?

You should do so. Focus on it and then listen to all your brethren who say, "I am saved by my faith alone."

James 2:17 Even so faith, if it hath not works, is dead, being alone.

Sincerely,

De Maria