Since this came up in a quest, and I'm not actually sure of the answers, I'm going to pose the questions here, to get an "official" stance. (and to pose my current understanding)
1) Are elementals alive? (I understand that they are.)
2) Can elementals die? (My understanding is that they can, but not by any physical means. To be specific, physical attacks only disable/dismember the elemental, rendering it incapable of cohesive movement, like attacking. Eventually, however, the elemental will reform.)
3) Do elementals feel pain? and would somebody that summons them know whether they do or not? (My understanding is that they know, in some way, that they are being damaged, but they don't necessarily feel pain as a human might understand it.)
Alrighty. There it is. Thanks!