"Lose 1 HP" is not damage and will ignore Block. However, it can be reduced by Tungsten Rod.
If the Necronomicurse is played, a new one will be added to your hand. While this means you can't escape the Necronomicurse, you can play it as many times as you want, and that interaction can be exploited in a number of ways. It allows you to take arbitrary amounts of damage in one-damage increments, triggering useful on-damage effects like Rupture or Blood for Blood; each play still counts as an exhaust, so it will trigger on-exhaust effects like Dead Branch, Dark Embrace, Charon's Ashes; and each one counts as a card played, so it can trigger things like Panache or A Thousand Cuts.