1. Important Rule 1: For a TPE Doll, only use oil. Never use Oil on a Silicone Doll.
Important Rule 2: Use Mineral Oil. (Or Baby Oil based on Mineral Oil. Check the ingredients)
I usually wash first, wait until she is dry, then oil, wait until the oil is absorbed, then powder.
I think oiling every three months should be enough, but this could change depending on climate and other factors.
2. If you handle the doll and have an oily feel on your hands afterward, then she probably doesn’t need oiling. And yes, clean first, dry, oil, let soak in, then powder. I put powder on with a big makeup brush – much easier.