You may be able to use the boolean plugin to 'chop' up your object.
Alternatively, you may be able to remove surfaces to 'break up the object' into sections.
Measure distance, select two vertices and read the distance from the information at the top of the control panel. This works on the vertices ofa line too - so you can measure the distance of the line.
To add text dimensions, use Tools->add-2d/3d-text.
Andy
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