Is one permitted to eat an entire “Pesach cake” (whose bracha is shehakol) right before alos (dawn), prior to davening Shaharis?
Does one fulfill the mitzvah of melava malka if he ate a “Pesach cake,” even though it contains no grain? (Although ideally one should wash on bread, I believe that melava malka can be fulfilled with other foods, as well, according to many poskim.)
Yes, this would have the status of eating any shehakol food before dawn, which is permissible.
Melave Malka should ideally be eaten with bread or Matza, however for one who has difficulty the Mishna Brura rules that fruit will also suffice for this meal. Pesach cake would have the status of fruit.
Mishan Brura 300:1, see here with regards to eating before dawn.