A couple of things to bear in mind:
You should handle -ve values with care with pow. You might clip, or mirror or do something else entirely. You may or may not have needs and control of your pipe so that you could do a round trip ...
The round trip, half to float is lossless, but as you point to, the other way is not, we are loosing bits afterall. There is care in the design so that the deltas are contained in frequent parts of the image.
Off the top of my head I can't remember if we published the docs on the number representations ... but there is a reference to the IEEE standard in the Technical Introduction that will shed light on the behaviour.
Piotr