This is going to be fun but difficult if you dont know what your doing.
Dont bother with A/C anything. You can easily plug something into a wall that uses DC (pretty much EVERYTHING you plug into a wall socket uses DC voltage). Its simple to convert AC to DC. All you need to do is use some diodes.
I found this on google images which saved me the time in having to draw it myself
This is a rectifier, it takes AC and makes it DC. Use this for everything. Your going to need highish wattage diodes though.
For the whole wall opening thing all you need is a servo with enough torque to swing the wall open. Do the math to figure out how much torque is needed in your servo. Consult this page for some guidance on how to do that: Link
Then from there it should be easy for you to hook up your servo correctly. To control the servo though all you need to do is hook it up to a micro controller so that when you press a button, it will close it if its already open, and open it if its already closed. We can help you more with this part once you have the other parts all worked out and such
If you need help with anything else, post it