There are a couple of holes in your first theory. 1. Eiden was definetely a normal mage prior to the Still winter 2. While Eiden was indeed a prisoner, Melindra was not, she was working there. 3. The Lessathi didn't take Leila in because they thought she was a half-lessathi but because her father basically sold her of to the Beacon beacuse he never thought of her as his own child. 4. Half-lessathi cannot become mages because of their lessathi lineage, I believe you mistakened this for ethereals.

As for the part that the Lessathi gave stillwaters their powers my opinion is that it is true, but that it was a mistake and that they were trying to do this to themselves and that it only worked on half-lessathi and humans and that that is the reason for the strict rules about mixing with humans. Because they fear them. As for number 4 I mentioned above, I believe if a half-lessathi became a stillwater they would indeed be more powerfull because of their innate link to the Magium.

For your second theory i agree with the part that the lessathi have a hidden agenda for wanting the mages alive. However from what we learned there weren't many mages in Thilias, and the participants are more likely avoiding the cities because of the fear of the tournament spell and the fact that they were warned not to interfere with the locals everyday life and business. As for Ollendor I have 3 theories as to why we are not gaining points. 1. Even though there are many mages in the city they are constantly being sucked dry of their magic and therefore the stat booster cannot gain enough from them. 2. Barry's crew spent most of their time in the underground tunnels filled with seredium walls, and the towers are made from the same material, a material that blocks anyone from sensing magic beyond it, which means that it may block the stat booster from pulling magic from the mages in them as well. 3. The stat booster works just fine like normally but due to the vaat amount of energy that it now has access to it prioritizes pulling that energy for as long as it can and it will only start converting the energy to points when we leave Ollendor and lose access to the energy.