Start with the simple stuff
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Well you have written a bunch of rules and most of them are non fatal if tested, so you start there. 

Objects are absorbed 
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Well I have a slight objection to that one: absorbed as in **encased and kept indefinitely** or **dissolved and excreted**? 

Test: Push a sewing needle into your arm. 

Success: Needle is gone after some amount of time. 

Failure: Needle causes discomfort, infection, inflammation or otherwise hurt you. 

Keeping safe from failure: Visit a doctor and have the needle extracted. 

Cannot drown
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Test: Jump into a pool at the shallow end and crouch down. 

Success: Still alive after 10 minutes with no ill effects.

Failure: Feeling the usual feelings of panic and discomfort of not being able to breathe. Starting to get grey-out and tunnel vision.

Keeping safe from failure: stand up and breathe. 

Cannot get fat
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Test: Eat excessively. Monitor your body temperature

Success: You do not get fat. Body temperature rises.

Failure: You gain weight. 

Keeping safe from failure: Stop over-eating. 

Fast healing 1
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Test: injure yourself lightly. See how long it takes to heal and if that varies depending on how much you eat. 

Success: wounds heal without scarring or discoloration, and they do so depending on your food intake. 

Failure: scarring results. Wound do not heal any faster compared to what they would normally. 

Keeping safe from failure: Stop injuring yourself

Fast healing 2
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Test: Cut off some part of yourself, like a centimeter wide flap of skin, as if say removing a birthmark or a mole. That cannot heal on a normal person without scarring. 

Success: The cut is healed without scarring. 

Failure: The cut is not healed without scarring. 

Keeping safe from failure: Sorry, you will have to put up with that scar. 

Fast healing 3
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Test: Donate blood five days days in a row. No normal person reacts well to losing five pints of blood in that short amount of time. 

Success: You do not experience dizziness or other signs of low blood pressure. 

Failure: You start to feel the symptoms of blood loss. 

Keeping safe from failure: stop donating blood as soon as you feel the least bit ill. 

Fast healing 4
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Test: Cutting off the tip of a finger

Success: the finger heals without trace of injury

Failure: the fingertip does not regenerate

Keeping safe from failure: again, sorry, it is gone... but a fingertip is easy to live without. 

Fast healing 5
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Test: Stab yourself in the lung

Success: you heal without sign of injury

Failure: you start experiencing great difficulty to breathe

Keeping safe from failure: call emergency services and have them patch you up at the hospital. Blame a mugging or something like that. 

Fast healing 6
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I think you get the idea by now...