First a question. Do you have a floating pad floor in your basement? If so, then your wall/door should hang from the ceiling, and not be built on top of the floating pad. These types of floors are common in most houses and the floor will rise and fall with the moisture content in the ground below. If you build on top of the pad and then the pad rises over the next few years, it will drive the new wall and vault door up into the floor above.

First and formost, check your local building codes and get a building permit. I know it's a royal PITA, but it will be worth it in the long run.

Over a reletivly short span as that, it MAY be ok to run a structural steel member across the tops of the adjacent concreat walls, I'm assuming they are part of the foundation and load bearing, and hang your wall and door from that. You'll still need to provide a gap at the bottom to allow for floor pad movement.

You might be better off, again depending on codes, to cut through the pad floor, add a proper footer, and then build a wall atop that and have it attach to the adjacent walls. That way it becomes an extension to the housing's foundation.

Do yourself a favor though, and check your building codes. Other wise, you might have to rip it out when you go to sell. Do it right the first time.

Good luck and let us know how it goes.