Diablo – Killing ‘Fallen Lunatics’ as a melee class

The Wizard will default to using their weapon if you are out of arcane power and attempt to use a left- or right-click bound skill that requires arcane power (i.e. not a Signature Spell). If you have a melee weapon equipped, your wizard will then run towards them to attack. If you have a wand, your wizard will shoot at the enemy.

Q1) This sounds like a bug, unless you have a spell bound to your left click that requires arcane power. I haven't seen this behaviour.

Q2) There is no way to change the "out of arcane power" behaviour of using your equipped weapon. You can hold down the Shift key to avoid running into melee an enemy if you are wielding a melee weapon but that only mitigates the behaviour, it does not change it.

Q3) You can bind the default attack to a left or right mouse button by removing that button's binding to any other skill (How do I set a mouse button to a regular attack?).

It's not required in the same sense that most stats aren't required. It's definitely one of the more beneficial stats if you have trouble kiting or getting out of the way of some attacks.

It's definitely possible to survive without it, but you may beat your head against a wall more than once.

The main benefit of movement speed comes from possibly being able to kite the faster mobs, and helping you out with late reaction speed or latency in terms of dodging attacks.