Hi there. I would recommend to work with 1/8 of the mesh. 1. Start with your basic shapes 2. Create seperate mesh that would act as boolean 3. Boolean 4. Rotate the mesh 45 degrees 5. delete 1/8 of the mesh 6. Clean up 7. Rotate back -45 degrees 8. Symmetri and voila. HERE IS THE 1/8th of the mesh cleaned
planarity is a new concept for me but while checking the support loops... i realised this deleting the two faces solved the problem. but i guess 8 edges were not enough for the hole, i had to increased the subdiv iteration from 2 to 3.