The Crystal Ball is a very rare item, this makes it powerful in the first place.
The character needs to first be attuned to the magic item in order to use it and from my understanding (on the DMG's page 159), while touching it you're able to cast scrying (with a minimum save DC of 17).
This doesn't come with any limits, you can use this as many times as you want during a day and don't need to be a spellcaster or have spell slots in order to use this (again: all you have to do is be attuned to it), you can read about this on the DMG page 141, Activating an Item: Spells.
No, you shouldn't suffer the normal ill effects.
There is a key difference in the wording that easily justifies a difference in the two scenarios. The Wand of Orcus states:
Any creature besides Orcus that tries to attune to the wand
Whereas the module states:
the Wand of Orcus tries to attune itself to the first willing creature
In the former case it is the creature's deliberate effort to try and attune itself to the artifact. In the latter case, it is the artifact itself instantly attuning to a creature which is willing to be attuned to, requiring no effort on their part. Essentially, a creature trying to attune to the wand versus the wand attuning to the creature.
I would argue that, mechanically, since you are not trying to attune to the wand (it is trying to attune to you), you do not trigger the negative consequences normally caused when trying to attune to the artifact. As the wand instead attunes to you, you end up getting the benefits of being attuned to the wand without suffering the normal consequence of trying to attune to it.
This also makes sense narratively; as an intelligent artifact, the wand normally desires to be wielded only by Orcus himself, and subjects anyone else that attempts to attune to it to some horrible necromantic energy. In the circumstances, however, it desires very strongly to be used to enact revenge upon Demogorgon, and so it will instead attune itself to the first willing person it can find. It doesn't make sense for it to try to kill or zombify that person, since that will make them much less useful at fighting Demogorgon.
It remains a horribly evil intelligent artifact, so anyone who willingly allows it to attune to them is certainly in karmic trouble in the long run, and they have to deal with the normal issues that come with wielding intelligent magic items that are in conflict with their own alignment/goals (which potentially includes being mind controlled by the wand). In the moment, however, you shouldn't have a problem - one assumes both character and the wand are united in their immediate goal of fighting Demogorgon.
Best Answer
You can not use it 24 times a day, due to attunement rules.
For attuning to a magic item one must spend a short rest:
Hence, if a Scrying fails and one of your companions wants to try, they must spend a short rest to attune to it. The time needed before attempting to cast another Scrying is then 70 minutes: 10 minutes of casting and 1 hour for the short rest. Your group can cast the spell from the Crystal Ball 21 times per day, not 24.
Pay attention that a person does not need to spend a short rest to unattune, once another creature tries to attune to the same item the first attunement ends (emphasis mine):