"She is gone" versus "she has gone"

When should I say "She is gone", and when should I say "She has gone" (and why)?

I think that when I mean "She went away and she's still there", it should be "She has gone". Are there exceptions where it should be "She is gone" ?

You should normally use be gone if no direction is specified, have gone with directions:

Where is Cleopatra? She is gone. (= she is away, or dead)

Where is Cleopatra? She has gone to the temple.

This is idiom: it is irregular and only applies to very few verbs. And is gone can still be used with specific directions sometimes, though it is probably rare. The opposite has gone without direction doesn't sound wrong, but it is probably less frequent.

I believe to be + past participle was used to form the present perfect for all intransitive verbs in older English, just as in other Germanic languages: not I have been but I am been, etc. So it was once he is gone always, even with specific directions, as in modern Dutch hij is naar huis gegaan. Then at a certain point in time the default auxiliary verb for the present perfect of intransitive verbs changed to have in English; but some old, very frequent expressions stayed in use, like to be gone and some others.

The word gone here is a predicate adjective, meaning "no longer here". Etymologically, it came from the past participle of go, but in modern English it is also an adjective. Like the adjective ready, the adjective gone cannot usually be placed before a noun. Compare:

The car was packed and ready.
*The ready car was parked at the curb, waiting for them.

When they looked in the cave, the treasure was gone.
*They looked everywhere for the gone treasure.

The Merriam-Webster dictionary does have examples where gone is used before a noun, but in most situations, placing gone before the noun is ungrammatical.

She HAS gone to the market

She is gone. (to mean, she left, she's away).

You can also use idioms like "what is gone and what is not...".... that is often used in literature.