I believe it's useless speculating on any science from science fiction, but it's fun, so I do it anyway!
The Technocyte theory seems the best to me so far, with the original (unconfirmed) theory of a continued Dark Sector game meaning the Tenno are creatures infected but not controlled by the Technocyte. This gives the being (and not the suit) the powers, but the suit gives them the ability/ease of access needed to channel these powers.
The one thing in common with all the powers (in this and almost any other game), is that they require energy. With enough energy and a sufficiently advanced tech (small electromagnets etc.), then most of the powers are acheivable - they were based off known behaviour after all. However, what this energy source is is more difficult. My guess would be a connection to the void which, unlike our interpretation of a void, is not empty of everything. Perhaps it is another dimension missing one of our fundamental forces? Anyway, perhaps this allows the Tenno to extract the energy needed to use their powers. A more realistic (but less exiting) theory though, could be really good batteries in the frame...
As a side note, the Hydroid puddle idea could explain stepping into multiple frames (perhaps each tenno has all the powers, but can only use the ones the suit is designed for)...
And another general discussion: what are your feelings on the void?