Use the light bulb test
In my mind, most of these questions can be answered by considering applying them to a claim for a patent for a better light bulb.
1) Inventiveness. The new light bulb requires some inventive difference. Maybe a new filament material or a new shape of bulb or something.
In my mind, trying all possibilities and selecting the"best" (least-worst) is unlikely to be sufficiently inventive. However, researching previous attempts, reading academic reports of different conducting materials, building a theory of how light emission works (even if it is wrong) can all be part of inventiveness. Even if those are analyzed by some sort of AI.
2) Effectiveness. The new light bulb has to work. So, it needs to be tested and the results analyzed and documented. In almost all cases, there will need to be many attempts, with results fed back into the inventive process to improve the invention. With current technology this is unlikely to be performed by robots, although it could be in the future and I don't think using AI or something for this phase would prevent it being patented.
3) Reproducible. The invention needs to describe how the invention can be implemented. This means sufficient instructions are provided to allow someone else to manufacture the invention once the patent expires. This is nothing to do with how the invention was developed or tested - just how the resulting invention can be built. This is the key reason for patents: the inventor gets a limited monopoly in exchange for releasing details of how to build the invention (but not how to reproduce their inventive process).
In these steps, AI could be a tool. But the inventor has to be a human - otherwise it is not inventive. And the invention has to be reproducible (but there is no requirement to document the process of developing the resulting invention - the AIs involved can be secret). In the old days, the inventor might have been the head of a lab employing hundreds of people (think Edison). Similarly, the inventor may use AIs - but they are just development tools.