The intention of the award is to allow you the freedom to devote 100% of your time to writing. You may use the award in whatever way that allows you to do this. However, it is Foundation policy that Institutional Overhed is not generally covered under this fellowship.
If you have a small amount of research to do along with the writing, such as updating some data, or follow-up interviews for a specific chapter, you can include this in your proposal. It should last no more than a quarter of the total fellowship period requested, and it should not significantly alter the shape of your proposal. You should be clear as to why this research component is necessary and what it entails, as well as what clarifying what research is already completed.
The Wenner-Gren Foundation receives over 100 Hunt Postdoctoral Fellowship applications and normally awards eight grants annually. Unsuccessful applications can only be resubmitted twice. A more detailed breakdown of various programs' success rates can be found in the Foundation's Annual Report.
No. You can apply regardless of your departmental or professional affiliation. However, funding decisions are made on the basis of the potential of the project to make a significant contribution to the field of theoretical anthropology. You must clearly demonstrate this potential in your application and also show a good knowledge of the relevant anthropological literature. It is not sufficient to merely use anthropological techniques (e.g. participant observation) to carry out research in your own disciplinary area or to carry out research in a non-western setting.