I am currently working to convert from ISO9001:2008 to AS9100 Rev D. I have run into a few road blocks and am in need of some assistance on how to complete. I am not sure what is being asked for product safety and how to go about performing a capacity and capability study for the process verification requirement.
The product safety requirements in clause 8.1.3 is asking for controls on product safety but is based on assessing the risks posed by the product through the life cycle. For instance, if your product includes a battery that could induce a shock on someone installing or using it, then what control processes do you need to plan and implement (such as safety caps to avoid shock, instructions in a user manual, safety processes in your production, etc.) If, however, you assess that there are no safety concerns for your product (such as a simple machining) then your assessment of the hazards would show not risks to be managed, and you can state this. This is why the requirement is stated, "as appropriate to the organization and the product".
In clause 188.8.131.52 on production process verification the requirement is simply stating that you need to perform any activities necessary to ensure that the processes you are using are able to give you products that meet customer and legal requirements. The note is just there to give you some ideas on how this can be done (notes are never requirements), such as the capability studies or capacity studies, but these are not required by AS9100 Rev D if they are not applicable to your processes or required by customers.