Move all items in group and sub groups to new layer

The bold is a no-no. They cannot contain competing visibility layers. They do, and of course you have visibility issues.

They are saved if the appropriate property boxes are checked for the scene in the Scene Manager.

The Layer Manager needs work. The settings are settable via the Ruby Console:
http://www.sketchup.com/intl/en/developer/docs/ourdoc/layer#page_behavior
Unfortunately, it be best to set the layer page behavior before making all the pages.

A page keeps a list of layers that do not have their default behavior. If a layer is not in that list, then it is set to its default visibility determined by one of these values:
LAYER_VISIBLE_BY_DEFAULT: 0x0000
LAYER_HIDDEN_BY_DEFAULT: 0x0001

To set it’s default behavior to hidden:

Sketchup.active_model.active_layer.page_behavior=1

For new pages:
LAYER_USES_DEFAULT_VISIBILITY_ON_NEW_PAGES: 0x0000
LAYER_IS_VISIBLE_ON_NEW_PAGES: 0x0010
LAYER_IS_HIDDEN_ON_NEW_PAGES: 0x0020

The “out of the box” setting for new pages, is to use the default setting. Or you could be double sure:

Sketchup.active_model.active_layer.page_behavior=0x1|0x20 # which is 33 decimal