You cannot gain more than 1 extra Summon from "Dverg of the Nordic Alfar", even if you Summon another "Dverg" with the extra Summon granted by the first one.
If you activate "Double Summon" while you’re able to Summon an extra monster due to "Dverg’s" effect, you still gain the effect of "Double Summon". Make sure to clarify which extra Summon you’re using if this happens.
You cannot Normal Summon an extra monster with "Dverg’s" effect if you Normal Summon "Dverg" during your opponent’s turn with "Ultimate Offering", but if your opponent gains control of "Dverg" afterwards, he can perform the extra Summon.[Notes 1]
If "Dverg" is Normal Summoned, then flipped face-down and face-up in the same turn, you can still Summon an extra monster.
If you Normal Summon them successfully, and their effects are not negated from the moment they step on to the field by something like Skill Drain, then for the rest of the turn their effect is applied, regardless of what happens to the monster.
Out of Date
"Dverg" must be face-up on the field when you attempt the extra Summon. [Notes 1]
If "Dverg’s" effect is being negated, you cannot Normal Summon the extra monster. [Notes 1]