Mouse drag and drop / drag to select animation in after effects
Expressions are you friend. Honestly I don't understand how anyone use AE without using expressions. To make the size of a rectangle shape follow a mouse you could do this.

Parent the mouse and rectangle to a null, with the top left corner of the rectangle aligned with the null. On the size property alt/option-click the stopwatch to open the expressions editor.

Delete what's there, and drag the pickwhip (the blue curly thing) to select the position of the cursor layer. 



the size property will now look like:

thisComp.layer("cursor").transform.position


(if your cursor layer is called "cursor"). Now when you move the cursor the rectangle will scale to match the movement. But there's a problem, it scales from the middle, so you can add an offset to its position to make sure it lines up correctly. This time we use a bit of maths as well. On the position property of the rectangle path (not the position property of the layer) alt/option-click the stopwatch and drag the pickwhip to the size property of the rectangle, and then divide that value by 2. It will look like:

content("Rectangle 1").content("Rectangle Path 1").size/2


Now your rectangle should resize as if it's beign dragged by the cursor. You might have to manually drag the layer to line up perfectly. You can use more javascript to make the layer start and stop following the mouse.

Go learn expressions. As a bonus (or perhaps as a negative) you get to learn javascript, a ubiquitous computer language.