League-of-legends – the max attack speed you can get

Yes you can by being in the fog of war, but you have to keep to the one side of it if you don't want to be spotted.

Clarification of the term "click to attack"

There are two key bindings related to attack:

• Attack move - default button A - when you click A cursor changes into target pick. Clicking left mouse button then makes your character either attack the picked target or run to the picked location and attack the first target that appears in your range during the movement. If there are more targets, it picks the closest one.

• Attack move click - default Shift + Right mouse button - it is a shortcut for Attack move

Advantages of using "click to attack"

• When you chase into a brush you start attacking immediately when you see the target
• When you missclick right button when lasthitting then you go in the creeps and get yourself out of position, that can never happen while using Attack move
• When lasthitting, Attack move checks for a target in a slightly larger radius than right click, which makes it easier to pick the target. It also might be an advantage in larger crowds of creeps when you need to select a creep precisely.

Disadvantages

• When using Attack move during chasing and clicking it on the ground, then if a different eligible target appears closer, you immediately start attacking it. Therefore, you obviously lose some time and even if it is miliseconds it may change the outcome of the chase.