Bad Cat? Or Sad Cat?

Koko on his back porch throne. It's warmish and dry there, and he has a cat door to come and go as he pleases.  

But he much prefers to be inside lounging in

front of the wood fire or the gas stove or snuggling with PK or me. The problem? 

He's taken to marking his territory, which includes inside our house. 

Koko is not really our cat. We started caring for him part time a few years ago when his "other mother" goes away for a week or two, which she often does. Like me, she has an elderly mom to tend to. We'd noticed him skulking around, and thinking he was feral, put out a cardboard box lined with warm stuff and tucked it under the eaves hoping he'd shelter. He did. We quickly learned he was friendly and needy and we invited him in. Eventually we learned that he had another home.

He wasn't really other mother's cat either, but "belonged"to neighbors who apparently mistreated him. Other mother reports that he plastered himself against a wall behind a bush, ears back and eyes narrowed, whenever he saw the mean-neighbor's truck heading down the driveway. (To their credit, the mean neighbors had him neutered and presumably immunized.)

Other mother adopted him, but he fended for himself when she had to leave. Then he found us. We've had a back-and-forth relationship with him and other mother ever since.

Koko loves the hunt, and he is most often successful.

He prefers other mother. He sleeps in her bed and loves to lick her hair and face, which she apparently enjoys. She also gets up several times a night (no cat door) to let him in or out and indulge his predatory night behavior.

Koko's food dish is always supplied, but he prefers his natural rodent diet, plentiful most months of the year.
Of course, he also prefers to devour his prey in the safety of our porch, sullying the mat on a regular basis.
He usually leaves the gall bladder for our viewing pleasure. 

At our house, he sleeps in the closeed-off heated living room in cold months, and during warm weather, in the back porch. We're not into cat catering at night, although I do admit to preparing chicken to augment his diet of mice and Meow Mix. When other mother's times away coincide with ours, we pay somebody to look in on him and make sure he's fed.
When we're away, and he's here alone, the cat door is always open to give him access to food, water, and warmth. Trouble is, other critters also enjoy the chow. We know that a feral cat comes in to dine and probably to spray. Either way, the stress of nobody home and the other cat are likely what's been causing the trouble.

Koko is proud when he kills a rat, but he never eats them.
A few times, he killed rats that had slipped into the house, chalking up big brownie points. 

Koko is the only cat that comes into the house, where we have lately found cat spray on many vertical surfaces. We've also scoured cat piss from walls and cupboards on the back porch. Not fun.

As I write, Koko is curled up on my office armchair, sound asleep. He looked so pitiful peering through the glass door in the chilly porch. I caved. I've closed the cat door to keep feral cat out and will try making Koko feel safe and loved and see what happens. Hopefully, no spraying.
If you've had a cat-spraying problem and resolved it, please advise.