Mage hand can pour out a vial of acid.

Pouring a vial of acid in this way will (generally) not damage an enemy.

It's exactly as the rules you quoted say. You can pour out the contents of a vial. Per the description of Acid, simply pouring isn't enough to do someone--who likely doesn't want acid poured on them--damage.

If you start pouring acid on one who doesn't want to be acidified, they can move, interpose an object, or otherwise evade the damage. In order to damage someone with acid you've got to splash it onto them, an activity that's defined as a ranged attack. And Mage Hand, per its description, can't effect damage on someone trying to not be damaged: it can't attack.

Could one pour the vial over an unsuspecting enemy, or one incapacitated or restrained, thereby causing them damage? I contend it follows the same rules: if you would need to make an attack roll, Mage Hand can't do it. Whether those situations require an attack roll--and therefore are attacks which Mage Hand cannot effect--is a ruling to be made by the GM.

No

Haste says:

That action can be used only to take the Attack (one weapon attack only), Dash, Disengage, Hide, or Use an Object action.

Casting a spell or using a magic item fall outside of those options. The rules on activating magic items say the following:

If an item requires an action to activate, that action isn’t a function of the Use an Item action, so a feature such as the rogue’s Fast Hands can’t be used to activate the item.

Additionally, it seems you have a misconception about the spellcasting rules. The rule that limits you from casting other spells in a turn only applies when casting spells with a bonus action casting time. For example, an Eldritch Knight could use Action Surge to cast fireball and magic missile in the same turn.

A spell cast with a bonus action is especially swift. You must use a bonus action on your turn to cast the spell, provided that you haven’t already taken a bonus action this turn. You can’t cast another spell during the same turn, except for a cantrip with a casting time of 1 action.