The problems you experienced occur with vanilla Hellfire multiplayer (and exist in the original Diablo as well if you attempt to enable SP only quests in multiplayer); sadly the quest specific code responsible for generating items in the dungeons or from NPCs as rewards are not synchronized at all and cause problems.
For Hellfire, only the player who turns in the quest reward to Celia will see the reward amulet generated, and if that player is anyone other than the host (or whoever is currently acting as host, if they left), it will disappear when they attempt to retrieve it. In general if you wish to attempt to interact with the quests/items at all, only the host should touch them.
There's also a bug with the Hive where the generation seed gets desync'd somewhere after creating the layout - many times in the Hive the players present will see identical level structure and paths, but the location of monsters, barrels, chests, and consequently every item they drop, is totally out of sync, which leads to a lot of monsters teleporting when activated on other player's screens, and nobody but the host can pick up items pre-placed on the floor or dropped by monsters/containers. Not really anything you can do but rehost and try again. It seems to happen less often if you visit one of the vanilla dungeons first before going to the Hive.
The good news is... if the host successfully picks up desynced quest/reward items, they can then drop the item and it will exist properly for other players who can see and pick them up. Excepting, of course, the ones that randomly vanish... I once had a very important item disappear in an Ironman game in vanilla Diablo, that was disappointing!
Hopefully some day we have an open source Diablo engine where all of the quests work properly in multiplayer. I spent some time working on them only to discover enabling them causes far more problems than I could fix.
[Edit: Corrected mis-explanation for what items bug out in desync'd Hive]
For Hellfire, only the player who turns in the quest reward to Celia will see the reward amulet generated, and if that player is anyone other than the host (or whoever is currently acting as host, if they left), it will disappear when they attempt to retrieve it. In general if you wish to attempt to interact with the quests/items at all, only the host should touch them.
There's also a bug with the Hive where the generation seed gets desync'd somewhere after creating the layout - many times in the Hive the players present will see identical level structure and paths, but the location of monsters, barrels, chests, and consequently every item they drop, is totally out of sync, which leads to a lot of monsters teleporting when activated on other player's screens, and nobody but the host can pick up items pre-placed on the floor or dropped by monsters/containers. Not really anything you can do but rehost and try again. It seems to happen less often if you visit one of the vanilla dungeons first before going to the Hive.
The good news is... if the host successfully picks up desynced quest/reward items, they can then drop the item and it will exist properly for other players who can see and pick them up. Excepting, of course, the ones that randomly vanish... I once had a very important item disappear in an Ironman game in vanilla Diablo, that was disappointing!
Hopefully some day we have an open source Diablo engine where all of the quests work properly in multiplayer. I spent some time working on them only to discover enabling them causes far more problems than I could fix.
[Edit: Corrected mis-explanation for what items bug out in desync'd Hive]