If a druid who had this staff were to wild shape into a bear, would the bears melee attack be able to trigger the necrotic effect and use a charge of the staff?

Quote from Razamis >>

If a druid who had this staff were to wild shape into a bear, would the bears melee attack be able to trigger the necrotic effect and use a charge of the staff?

 No, you have to attack with the staff to trigger the necrotic damage.

said druid would have to drop the staff first because when you beast shape everything worn and carried is basically invisible/protected/unusable while transformed. Read wild shape carefully. 

Does "Steel Wind Strike" enable the "On a Hit" effect with this staff?

Steel Wind Strike mentioned a "Melee Spell Attack" but also uses the "On a Hit" term in the spell...

Imagine if it does possible 5x 6d10 + an additional 3x 2d10 total damage output of 36d10 damage :D unless I'm reading the spell wrong or the rules doesn't enable the staff to activate.

the spell doesnt explicitly state you hit them with the weapon (which would allow the staff of withering to discharge) but any sane player or DM should assume that yes, you do hit them with the weapon, and such should be able to discharge the staff, although i sincerely feel this is a terrible idea

Steel Wind Strike is only for wizzard and ranger 

the staff is not 

This item pairs particularly well with Shillelagh! Take this as a Druid, or as a Nature Domain Cleric or a Pact of the Tome Warlock, and you're laughin'.

Does the disadvantage apply on every hit, or just when you expend a charge?

In my game, 100% yes

said druid would have to drop the staff first because when you beast shape everything worn and carried is basically invisible/protected/unusable while transformed. Read wild shape carefully. 

You might already have done so by now, but if not, you might wanna follow your own advice, because this is what it says:
"You choose whether your equipment falls to the ground in your space, merges into your new form, or is worn by it."

It then explains that any equipment can only be used or worn if your new form's anatomy allows it.

This would be a great weapon for a monk. If only they could take it...