I'd say the power is adaptation depending on what's needed for survival. When being first attacked, the power manifested in a zone neutralizing the powers of other mutants, eliminating the immediate threat. Then, upon his first contact with Rogue, this ability became more concrete, to defend himself from her abilities.
The second time he got into trouble and got injured, the power kicked in the one way it could - rapid healing, which Null had seen Laura do, and even remarks her powers being on his mind.
The third time we have the Sentinels. At this point Null think that draining power might work, so the adaptability kicks into Rogues powers. Sure it doesn't work, but this gives us a hint on how the ability might work. Null either needs to witness the power being used, understand how it works conceptually, or needs enough physical contact for his body/mutation to learn how the other mutation works and mimic it.
The fourth time we see that the abilities he has mimicked have matured, and are now a part of Nulls own arsenal. Naturally he has limited control over them, thus its all out, but regardless, we see that the powers are retained. This part makes me think he might be something akin to "En Sabah Nur", better known as Apocalypse, albeit far less power hungry or, arguably, evil.
But that's just my theory/guess as to it.