1. Not at all, your recommendation letters can (and should) come from people who know you. A good mix of both academic letters (from past professors you've worked with and studied under) as well as legal employers. Your letters should reflect some interest in law teaching as well as in policy and academia, as those are topics most emphasized by Yale.
2. Yes having a Ph.d is an added bonus, especially a non-legal Ph.d. can go a long way in showing your interdisciplinary capabilities which I think will be appreciated here. Note however that having a Ph.d. is not a pre-requisite in any way.
3. So academic experience, past publications, past work in law teaching - are all things to include. Similarly work in courts or with government, anything public sector and policy oriented or juriprudential - is highly advised. Note that you want to be able to explain what your academic agenda is (there is an essay that you need to write about that), and your cv should reflect that academic agenda.
I hope this helps, and please pm me if you have any additional questions.