In the Septuagint Uriah the Hittite is Ourias Chettaios. I think the term Hittite used of Bronze Age Asia Minor is just the English rendition of the name based on Hatti (an earlier people who spoke an unrelated non-Indo-European language before the Hittites of the 2nd millennium BC showed up).
Nope. The OT term was already being discussed as an historic people before the discovery of the so-called “forgotten empire”, the capital of which wasn’t discovered until late in the 19th c. The term Hatti is now used to refer to non-Hittites, in part due to the circa 1930s cracking of the cuneiform archive (by Emil Forrer I believe) which found NO trace of any language by that name (Hattish, Hittite, etc) even though the names had been clumsily applied.
Most of the problems stem from the fact that the conventional pseudochronology is dead wrong.
https://en.wikipedia.org/wiki/Hittites#Biblical_background