The answers would depend if gravity is a Quantum field or not
1. A graviton could give rise to another (albeit lesser) graviton, thus increasing the total gravitational energy.
Not sure what you mean, lesser particle meaning a different particle? If you mean a graviton with a different value, in a Quantum field it's not possible as it would be quantized. For example every electron has exactly the same value there is no such thing as a lesser value electron. All particles in Quantum fields are quantized to exact identical values and as that process extends up, you build the concept of an atomic table where each atom of each element is identical except for isotopes.
2. A graviton might convert into a number of lesser gravitons, thus increasing the number of gravitons, but not the total gravitational energy.
Really same as above, explain what you mean by lesser graviton?
In a no Quantum field situation I guess a graviton could be any size it would be controlled by whatever theory was at play. So I guess under such an idea it could vary from nothing to the size of a black hole unless the theory somehow imposed size constraints. Is that the situation you mean?
I can't answer the last bit unless I understand what you meant above.
The graviton page has been brought up todate and it would be worth a review
https://en.wikipedia.org/wiki/GravitonThe bit that might interest you is how hard gravitons are going to be to detect individually and possible problems detecting even a gravity wave.
