About Kadaj (spoilers)

[Masamune·1600]

Kadaj, effectively, really does turn into Sephiroth.

Kadaj is a Remnant of Sephiroth. This means that, as was also the case with Loz and Yazoo, he was formed when Sephiroth's body was blown apart following the final chain of events in the original game. Having been formed from Sephiroth, the three SHM are Sephiroth, in a sense, and instinctually desire to merge with JENOVA cells, which Kadaj does.

Sephiroth is, effectively, almost indistinguishable from JENOVA, as he was given JENOVA cells while still in the womb, and has thus become the conscious embodiment of JENOVA's immutable aims. The aims become more complicated in Sephiroth, but stay true to the quintessential "needs" of JENOVA.

This matters because Sephiroth's will is more important to his identity than his body. His identity is bound up in his personal perception--the silver haired man with the long sword--but the shape-altering qualities of JENOVA can replicate this completely (as seen with the Sephiroth forms encountered throughout the original game). His will, however, even though identical in fundamental goal to JENOVA, is unique, and therefore is necessary for JENOVA to fully manifest the form of Sephiroth. In being Remnants, Kadaj, Loz, and Yazoo also manifested the thoughts/will of Sephiroth. Hence, Kadaj and the others are unknowingly subject (to a degree) to Sephiroth, embodied in their desire to bring about "Reunion." When, then, Kadaj merges his physical body (the biological material of Sephiroth, and, more importantly, the manifestation of Seph's thoughts and will), it is possible for a fully real Sephiroth to again realize himself on Gaia.

What this means, in the long run, is that Sephiroth can only truly die when all JENOVA cells are eliminated, and/or when it becomes impossible for him to manifest his will on Gaia. Some JENOVA cells likely still exist following AC, but it seems unlikely that there is any obvious way for Sephiroth to use them to again manifest himself.

As to the container, Joel, there is a point while Kadaj is falling (just before he "becomes" Sephiroth) where he plunges the contents of the container into his chest. Thus, he merges with the JENOVA cells, and Sephiroth returns.