I've never had any issues pulling keys off mine. I find the easiest way to pull the space bar is to pull the keys on either side, and then use my hands to pull it up from both sides simultaneously.
There are no visible stabilizers, at least of the wire variety. For the space bar, at least, there are 2 stubs underneath, on either side, that slot into those different looks "switches" on either side of the white rubber pieces that provide stability.
Hope that helps, and welcome to geekhack!