Straight to your questions:
1) I assume that you have not updated the tooltip along with the target control - please update the tooltip as well along with its target and see whether this fixes the problem. The tooltip control detects when the target is updated in most cases but in some specific cases it is needed to update it as well as you would do with any standard control when you change associated control.
2) The behavior you describe is the natural behavior when you have an element which is child of another element. The very same behavior can be reproduced with standard DIVs and this is how the things work and it is not directly related to RadToolTip. That is why we have provided the RenderInPageRoot property - a demo is available here:
This being said, your scenario requires setting the property and this is what you should do.
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