(1) Yes, it is;
(2) «Veglia» in this case means the event to «vegliare su un defunto» («keep vigil over a dead man», «watch over a dead man»), whereas «wakefulnessis» is the inability to sleep («insomnia», «sleeplessness»);
(4) At this dramatic moment, when the poet is watching and touching the corpse of his dead friend, he is feeling a strong «attachment to life» («attaccamento alla vita»), for this reason (3) he writes «lettere piene d'amore» («letters» in this case means «words», not «missives»; «words full of love», not «missives about love», which compose this poetry).