Mine does all of the above. In fact my vet even said "you'd think she's part dog". Do any of your cats chew things? For example, headphones, cell phone chargers, any thin cord really, cardboard boxes, wood from a door, yes, wood off of my door.
Both our bathroom and bedroom doors have strips of wood peeled off from them from Rampage biting them. She is declawed so she didn't scratch at them. I've bought some spray that we're not sure is even working because sometimes she does it, and sometimes she leaves the doors alone.
We've also duct taped every cord/cable in the house because of her history of biting through stuff. I've lost 5 pairs of headphones, 2 phone chargers, almost my dustbuster charger, set of big stereo speakers... there is probably more. lol..
Luckily, she has not hurt herself doing any of this... (knocking on wood).
She went through a phase of this when she was younger and then it seemed to go away, but my boyfriend and I went to Montreal a couple weekends ago and left her for 4 days (my parents came over to check on her every day), which is the longest we have ever left her and we came back and the wire on our stereo speakers was in half. Luckily my boyfriend was able to fix it.
I'd be interested to know if this has happened to anyone else? My cat has caused more damage in 1 year than the 6 dogs I've had over 20 years put together!