I think a lot of your questions can be answered here (including the other pages that these pages link to): http://www.openphilanthropy.org/research/our-process and http://www.givewell.org/how-we-work/process
Because our fund managers are all GiveWell and Open Philanthropy staff, we inherit their methodology. If in the future we move beyond GiveWell and Open Philanthropy fund managers, we'll need to have pages on their process too (and how it potentially differs from GW / OP).
A more accessible introduction to how to assess which problem area is most important is here: https://80000hours.org/career-guide/most-pressing-problems/