Yes. The prefix "cis" stands for "within" and "trans" means "outside". So, "cis-Neptunian" means "inside Neptune's orbit".

Because it spends most of its orbital period farther from the sun than Neptune is.

It is any natural body past the orbit of Neptune. (e.g. Pluto, Eris, Sedna)

The most recent change is probably the demotion of Pluto from "planet" to "trans-Neptunian object".

Pluto is a dwarf planet and trans-neptunian object. Crossing orbits with Neptune stops Pluto being a planet.