Tombstone Stairwell

This has the supertype world. When a world permanent enters, any world permanents that were already on the battlefield are put into their owners' graveyards. This is a state-based action called the "world rule." The new world permanent stays on the battlefield. If two world permanents enter at the same time, they're both put into their owners' graveyards.

Does not put the Zombies onto the battlefield if this card is not still on the battlefield when its ability resolves.

All the tokens are put onto the battlefield simultaneously.

If something changes the names of the tokens, then the "at end of turn" ability will still destroy them.

You control the triggered ability, but each player controls the token creature they put onto the battlefield due to the ability's effect.

Both the cumulative upkeep and the triggered ability trigger at the beginning of upkeep, so you can choose what order they resolve.