I'm a bit surprised no one has replied yet, but let me ask a few questions.
First, is there any rules/bylaws/agreements/ that govern what you can do in a common wall. That question needs to be answered before you start any work.
Don't know of any laws that would dictate what can be done in the common wall. At this point I am guessing after talking to a local plumber over the phone, he said that it can be done and quoted me $750 to move the plumbing for me. The bathroom main light fixture is located in the common wall above the mirror and the current sink so I am assuming that the wall is not untouchable. I am planning to cut out a piece of drywall in this wall and see whats in it first before I'll do anything.
What do you mean (exactly) by "my... sink is located between two walls"? Is this some kind of alcove? Does the new sink fit? Why did you purchase this sink before you knew you could use it?
My sink is 60" wide and located between two walls on the left is small closet (with all of the plumbing going between floors. This bathroom is on the second floor of my condo) and on the right is a wall that has a bedroom closet on the other side. The new sink will fit as its also a 60" wide but little taller at 36" tall. I got this one as its 3 piece unit 18x24x18 where the 18 " are drawers and the 24 is the sink part this way I'll be able to carey all of this by myself upstairs to set it up.
Can you shut off the water without shutting off the neighbor's water?
Yes, I can shot the water to my unit only. I have my own boiler, furnace and the water meter in my garage.
The actual work is possible, even routine for a plumber. You also have the possibility of running the plumbing around and behind the drawers.
Yes, if I don't feel comfortable dealing with the common wall I will attempt to run the plumbing between the drawers where I have 3 inches of space between the drawers and 1 inch of space behind the drawers. I would just prefer to have the plumbing come out of the back of the vanity as most vanities on the market are designed for.