1. is it possible to move the mouse based on the grid size (let's say 16x16) instead of having a normal fluid movement?
So do you want the mouse to move in 16 pixel increments? I am not sure if this is possible as Construct only reads from the mouse it cannot control it.
As for the example I provided you can move a sprite in pixel increments based off the mouse movement however.
2. is possible to draw a series of squares based again on the grid size with a distance between the mouse pointer and a sprite?
This is possible you will need to calculate where to place the sprite based of the grid size (16x16) and the viewport size. You maybe need to look into pathfinding or see if you can use the existing pathfinding plugin.
It's difficult to point you in the right direction without a grasp on what you are trying to achieve. Maybe you could clarify your image you provided and what it means?