Both of these abilities are static abilities that generate continuous effects. That means that these abilities will always apply as long as Elesh Norn, Grand Cenobite is in play and nothing causes these abilities to be removed. These effects are applied to the appropriate creatures as soon as they enter play. This means that a Leonin Skyhunter creature you control will enter play as a 4/4 creature. It will not enter as a 2/2 and then become a 4/4 creature.
Similarly, creatures controlled by your opponents will enter play with the -2/-2 effect applied to them. An opponent’s Ember Hauler will enter play as a 0/0 creature. Because state-based actions are checked immediately after spell or ability resolves, this Ember Hauler will go to the graveyard before anyone can play any spells or abilities. This means that the controller of the Ember Hauler will not get the chance to activate its ability and sacrifice it.