Taking this at face value, I'd say that this magic specifically affects something related to or containing a specific quality that happens to only be in biological material. This would easily cover why it only really seems to be able to manipulate and alter the properties of certain things over others. For instance, maybe this magic can only embed itself in these materials, or there is already something in these materials that the magic can work on.
As for why it cannot allow people to do something but not others, that is far more of a complex question. After all, the idea of "shooting lightning" or flying could theoretically be achieved by altering the body to have that capacity, just as much as it could be done by manipulating external factors; that it can do neither in these cases implies that it cannot vastly alter the baseline functions of a subject's body.
So going from there, it's pretty easy to see where the limit lies from your examples.
- Moving around and restructuring biological materials.
- Manipulating a body's systems (likely by triggering or inhibiting specific responses)
- Grow more biological material.
- And creating artificial creatures.
None of this requires more than being able to move around certain materials in complex ways and instigating the growth of new materials. Once you can do that, all those other abilities fall into place. Many things can be done just by using that movement to trigger or inhibit specific responses the body already has (alteration of emotions, senses, health, generation of seizures, and instigating specific behaviors). The "interface" ability depends on if it is two ways or not. If it is one way only; then all it takes is one individual to force another's brain to think whatever "message" is being sent to them. If it is two ways, then in addition to that capacity, the sender would have to be able to sense and interpret the other's signals; which isn't a stretch since it would be hard to manipulate their biology without having some feedback to work with.
The other abilities just come from being able to grow biological material. This would help reshape tissue, grow new appendages, or create "golems". However, this implies that what new tissue you can grow is limited to only having common functions (hence the lack of certain abilities like shooting lightning, telekinetically manipulating metals, teleportation, etc.).
Finally, the inability to fly implies that while you can move and manipulate biological material, it cannot be done with a force strong enough to lift something with the weight of a human off the ground (at least long enough to consider it flight).