If a non-Human creature you control without a +1/+1 counter dies at the same time as Mikaeus, that creature’s undying ability granted by Mikaeus triggers and will return it to the battlefield.

If a Human deals damage to you at the same time that Mikaeus is dealt lethal damage, Mikaeus’s triggered ability triggers. That Human will be destroyed even though Mikaeus has left the battlefield.

Any damage dealt to you by a Human will cause Mikaeus’s ability to trigger, including noncombat damage dealt to you by a Human and damage dealt to you by a Human you control.

The +1/+1 bonus that Mikaeus gives to other non-Human creatures you control isn’t a counter. It won’t prevent undying from triggering.