Welcome to PT.
The first thing you need to check when a cat is urinating inappropriately is if there is a medical reason, such as a urinary tract infection. If you are able, can you get him to the vet for the simple urinalysis? In addition, he should be tested for FeLV/FIV (snap combo test) or else he can put your own kitty in danger of these two contagious and deadly conditions.
Does his urine smell strong and musky? Like a strong sour smell? If so, you are probably dealing with an un-neutered male. He will have visible testicles and his face might be very round with large jowls. I hope your female is fixed.
Being declawed doesn't necessarily have anything to do with inappropriate urination, but can be related to unwanted biting.
The other behaviors you describe make it sound like kitty has too much territory to deal with at the moment. It's best to keep his area small, such as a bedroom + bathroom only. You must have a litterbox in there and his food and water too.
Cats knocking stuff down is just a part of everyday cat ownership. Just because you may be used to a cat that doesn't do this doesn't mean it isn't a widespread behavior. I suggest you take your breakables and valuables down to a safe level or safe place. He is getting used to territory and exploring everywhere and everything. This will most likely subside when he learns about every object in the room.
After an isolation period of around 10 days, you should be seeing him 'decompress' from his frantic behavior. Then, you can increase his territory of the house, and he can go to sleep in his original safe room. He should be introduced to your female slowly and carefully, only after he is comfortable with his surroundings.
And, if kitty does not like being petted on his tummy, then don't do it.
Most cats have a sensitive place on their bodies, it's up to us to be sensitive to them.
Thank you for taking him in from the cold.
Hope this helps.
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