LOOK at the specs on the cabinet you purchased. Four inches is fine, and it floats, so getting underneath the clean a floor is not an issue. Dust goes to the FLOOR. Yes the drawers must clear a door frame....if the drawers are full overlay, or if the frame is less than the thickness of your casing, which I doubt, and can't be seen in your photo. More important, there needs to be sustantial support in framing the wall behind the vanity and often a side as well. Read the install specs or get a pro. You just don't screw it to a wall, or even a stud. You'll tear the wall down: )

When placing vanities you are correct, you have to pull the cabinets off of the wall, especially with a full overlay door so drawers will open. Make sure vanity is properly supported. Federal Brace makes vanity brackets for floating vanities that will hold up to 200lbs, in case your vanity doesn't come with a support system.

Thank you - I am having it professionally installed, so I'm not too worried about it staying up, I'm more worried about leaving an awkward gap between the side wall and vanity. If there are 4 inches between the wall and the vanity - will it be difficult later on if, say, I were to re-paint the bathroom? i.e. how do you paint the wall when there's so little space? or will there be dust and dirt trapped in the gap that would be hard to clean? (I'm not worried about cleaning underneath it - that's what swiffers are for). I realize dust hits the floor, but if you've ever seen the space between my oven and the countertop/cabinets, you'll know what I mean about dirt getting stuck there. (OCD here!)