When I special summon light monarch kuraz with heavenly monarch Ehther's effect, I can't pop 2 cards on the field like Kuraz's effect allows to do so.
Is the special summon of Kuraz the last thing to happen? It can miss timing. A common example where this can happen is summoning Ehther by tributing Edea.
Yes, it is indeed the last thing to happen. For example: it's the enemy's turn. They lay 2 traps face down, and summon a monster. I use Ehther and summon him with his effect. Ehther's effect activates, I send the 2 monarch spell/trap to the grave, I target kuraz, kuraz is special summoned and then nothing. Kuraz gets no effect and the opponent simply proceeds with his turn.
I've been having the same problem with Delg the Dark Monarch and Kuraz. doesn't matter If it's in my turn or my opponents, their effect wont activate when they hit the field. Also I've never been able to target use Kuraz to target himself when he's tribute summoned. Any resolutions so far??
Missing the timing is a complicated issue, and we need more details about the situation. Preferably replays, or at least screenshots. I can tell you, that it appears to work just as intended on my end.

Kuraz being unable to target himself, if he has been tribute summoned, could be caused by March of the Monarchs. It blocks not only your opponent's but also your own targeted effects.