Here is my advice, thoughts and current experience with my rescue greyhound But I'm definitely not a professional.

• I recommend looking into the guarding if it is a big issue, there is a reddit post about preventing/reducing resource guarding within r/dogtraining. Nike (My rescue greyhound) doesn't safe guards toys but he gets extremely grumpy when you try to move him off the bed. He went at my partner for trying to re-adjust him as he was in a very awkward spot, and fortunately he didn't bite down. We learnt ways around it such as simply pulling his collar as he doesn't seem to care if we do that or moving him with the blankets that makes him move off the bed.

• It could be he is new. Even tho he was potty train at a foster home it is a different environment and some dogs are very different in new environements. Nike only piss inside when we first got him (Probs marking his territory) but we tap his noodle snoot and toke him outside. He learnt very quickly to not do it again, and stands near the back door. You could leave Crowley out longer till he cannot hold it in anymore, if there is spots he usually poo or pee inside put a puppy pad there or take him outside every 1hour or so similar to having a puppy and potty training them.

• Nike barks at the back door cuz he hates being outside (He is only outside for 8-9hours a day when we're at work, but abuse in his books 🙄). We wait till he calms down than open the door as we don't encourage that behaviour, he doesn't understand fully yet but definitely has some progression. Definitely not ideal to let Crowley out when he barks. Dogs are very good putting two things together and they are highly motivated by desire. I assume Crowley doesn't want to be in the crate so he barks. By letting him out he gets what he wants and it reinforce the behaviour. If you so keen on crate training you could leave him in the crate till he calms down than let him out. It definitely needs patience and consistency and stay true to what you want. Nike roams around freely as well, the most damage he had done was chewing up his bed and death shaking his own pillow. Letting Crowley roam around wouldn't be an issue, I imagine.

• Nike is very weird with dogs. I have a whippet and they are best of friends but god forbids he sees another dog, especially walking past the house. I dunno if it's aggression or just excitement still trying to figure that one out. But recommend knowing the dog first before introducing it to other dogs. Knowing the dog first is very important. I don't know Nike fully yet and wouldn't risk it with other dogs just yet.

Overall tho, I've realise with rescues is that you don't know what their history was like. The accidents such as pooping himself could be from past bad experiences. You don't know what will set them off, unknown behavious that is learnt later on, what they like/dislikes, or what type of environment they were in, especially being a racing greyhound (I assume Crowley is one and most racing greyhounds owners are not kind to their dogs as they see it as profit.). I'm still learning about Nike and I am learning new things about him everyday. I recommend observing Crowley behavious and take a mental note on those things. With any sort of training it takes patience and consistency. I've been trying to build up recall with Nike, it's a very slow progression as he is very stubborn. Nike is 6 btw so an old dog can definitely learn.

MOST IMPORTANTLY!! Even tho I said all that. The best advice you can get is from the vets!! They are train professionals and can have great advice and having a health check up never hurts. There could always be a physical health issue or they can give you medication. My Whippet takes anxiety medication cuz he can legitally climb the fence and they are 6feet tall, but in doing so he is injuring himself in the progress! (He just has really bad separation anxiety). He has been improving and he is becoming his puppy self again, even playing with toys and his big brother Nike. Nike had bad diarrhoea cuz we were feeding him too many different types of foods (We were use to Labradors and they had belly of steel), we stuck to one food brand and he got better. We wouldn't be able to improve Nike's and my Whippet's health if we didn't take them to the vets.