HHMI Investigators are supposed to be some of the most innovative medical scientists there are. I'm not linked to any HHMIs but I think the selection process goes something like a solicitation for NIH-Request for Proposals (Invitation-only grants). Often, they are on a particular topic and proposals are submitted. Only the very best get chosen.
Not really. Selection is by solicitation of nominations from current HHMI investigators, department chairs, etc. It is VERY political and nepotic, and based on the individual, not any grant they write. You can appreciate this if you look at the pedigrees of many HHMI investigators, they very often trained under HHMI investigators themselves. Also, there is a huge concentration of HHMi people at certain prestigious universities, while some decent institutions have next to none even though they have some great scientists. This is not to say that HHMI people are not in general very productive and creative, they certainly are. They also have a lot of money, which of course fosters productivity, and is another reason they are good to train with.