Here is the space where my vanity will go. The vanity i'm planning on purchasing is below. How can i fill the gaps on the face and on the top?
This is a free standing vanity. It is not made to finish against a wall. The cabinet part does not lend itself to adding what we call "fillers" as a standard vanity cabinet would. The open shelf on the bottom is the main culprit for this.
Anything you do to try and add onto the countertop itself is going to look bad- it will look like what it is- an unnecessary add on.
You are better off to just do a good job on the drywall repair and mount your cabinet/ countertop as it was designed to be installed- centered between the walls with a space on each side.
I cannot see any way to make this look better than that.
Otherwise, get a 48" standard box cabinet and 2- base fillers which you cut down to 1 1/2" each to fit wall to wall. Then procure the correct size countertop (and matching backsplash).