LOX:
Several comments for you to help with your problem:
Your use of layers is not correct. SU uses layers for visibility control and not geometry isolation like cad programs. Enter the edit context of a component and select say a line( primitive geo.) the entity info should report layer 0. You have assigned them to other than layer 0 and IMHO contributed to some of the selection problems you are having. I consider this make play change.
To correct select ,say for example, the wall layer and then the - and then the option to move to the default layer, then recreate that layer, then with the entity info open select each of those components and now assign the component to the wall layer, repeat for the rest of wall and other components;
You should be aware I think there is a bug in SU8 and 2013 as reported here. http://productforums.google.com/forum/#!category-topic/sketchup/technical-problems/SX9LgRqek1c. If you enter the edit context of a component make sure the you place the drawing axis correctly because it can skew depending on how you have the component axis set. I think that caused some model errors for you. Hope this not an artifact from my set up.
Moving the model back should be done although I cannot verify the same problem as you unless I regress back to SU7.1+ ,but it should be done because of SU 32 bit floating point and the associated calculation precisions inaccuracy with the large numbers.
The Su component definition is invariant under, move, rotate, scale operations so you could make almost all the walls 1 component. Not necessary but would reduce model size a little.
Making the "hanger" all 1 group with nested components would also help but not necessary
