mother: *xanos, *xana, *hana, or *ana?

*xanos - IE

*matêr - IE - *ma with the kinship signifier, right? And, if so,
why
create another word for mother? Was it just a baby-talk thing?

*ana - Uralic/Altaic

I've read both *hana and *xana to be recostructions of the non-*ma
mother word. (Are they supposèd IE reconstruction[s] other than
*xanos, or is it/are they supposed to be Anatolian reconstructions
instead?) I'm assuming IPA is being used here, in which the /h/ and
/x/ would have slightly different pronunciations. Is this the case,
or is using "h" or "x" merely a written preference by whomever was
writing?

Hannahanna - Anatolian, meaning "mother's mother" - So, would it be
logical to deduce that Hanna would mean plain "mother" in Anatolian?

...along with others I either can't remember or don't know.
Apparently, going along with an earlier discussion of the
Anat[h]/Anahita/Neith/Athena/etc., in Canaanite (or Hebrew, or
Phoenician, or whatever it's called), was Channah (or however one
prefers to spell it) merely an epithet for the mother goddess, or is
it a direct derivation from the word for mother? It apparently is
supposed to mean something along the lines of
"grace/mercy/favor/pity", though only "grace" is usually used as the
meaning, as far as I'm aware.

Could anyone tell me the Sumerian, Akkadian, Persian, and/or
Hebrewish
mother-word cognates?

And what, exactly, was the at- prefix on certain Greek names supposed
to designate?

TiA!,
Eris