1. Didn't really had time to use them, but I think you will have to handle some kind of custom UIDragObject : http://www.tasharen.com/?page_id=893
2. You have to unselect 'Automatic' from UIRoot (the UI scales with the resolution), set your default scale and then use UI/Anchor/UIStretch to manage the Widgets positions/scale.
It is up to you. Widgets under a GameObject with an UIAnchor attached to it will be anchored to that point and will keep the same size in pixel. There are 9 points available.
Why would it change the width? o_O Are you trying to skew your UI?
Manual height of 1136 means your UI components will think that they are always being used on a screen that's 1136 pixels tall. Strange height...
By using anchors. The UI has to be modular. If you only have one UIAnchor (as you get with a default UI layout), then everything will remain at the center.