I believe she work exactly like fire main and Kushina habanero. She suppress immunity and cause immobile until the end of the round. The only thing that last until the next round is her chakra sealing. So if you use it on edo Minato after his standard he gonna be immobile until the end of the round and not the next round because he has immunity. On the other hand, if you use it after standard on a ninja who doesn't have immunity like kakuzu, he's going to remain immobile round 2.

Also, ninja who have a immunity buff like light main, will react to this debuff the same way Edo Minato reacted to it.

True, though I had once a fight in Arena against Edo Minato that recovered from Immobile at the end of round 1, despite the fact Kurenai used her mystery after his standard. On different game, it worked as intended so I dunno what is happening.

In general I think immobile, Chaos and Sleep effects are unreliable, I had many battles where they didn't do a thing as they were applied after target's standard attack in Round 1 and stoppd working before standard in round 2. I don't now if it is due to some bugs or *a hidden mechanics.

Kurenai summer should be fixed or her passive rewriten, because a groupmate of mine got her recently and got very disappointed.
Indeed, the target will only be supressed two rounds ONLY if you supress him after he's used his standard attack, in some cases this is not really an issue but in others it just makes the difference between winning and loosing. I wouldn't buy a ninja that makes you wait to see what your opponent does first, reaaally bad idea.

But it doesn't make sense... If weaker debuff like Sleeping can overwrite stronger like Immobile, then Summer Kurenai can counter herself, which is increadibly dumb.

Is her sleep 100% chance like regular Itachi?