Meter stick.
If you have the equipment you can film the bounce with a height metric in the background so that the cameral will catch the object as it bounces up against the height metric (e.g., a meter stick). If the camera is really special and you can take slo mo pictures that's even better because you can see the exact moment the object reaches max height on the meter stick. A less precise method would be to time the fall from the max bounce height. In which case the height the ball fell from would be calculated as h = 4.9 T^2 where T is the timed fall in seconds and h is the bounce height in meters.
rubber ball
yes
If you mean measure height then it would be the metre if you mean measure weight it would be Kilograms
With a tape measure.
metres
ruler
No, it would bounce better on warm days because heat makes things exspand and cold makes thing shrink
kilometers
Metres.
You would use meter's to measure an oak tree's height.
A measuring tape or a laser distance measurer would be suitable tools to measure the height of a ceiling.