How is Stray and Damian’s relationship? How’s her relationship with Alfred?
Stray and Damian get along pretty well, all things considered (the things being the fact that she grabbed him when she and Jason were going back to Gotham after Jason came out of the pit, and the fact that despite being taken to Bruce much earlier Damian is still a very serious kid).
Stray put Damian firmly in the little brother category and does her best being the irritating order sibling to him and Tim, who have no choice but to join forces against her and Jason's combined efforts.
Damian does respect her skills, even if her silly behavior and the wesk little kid facade confused and irritated him at first. Stray is the one to introduce him to the art of getting away with things by being small, and cute and polite, and the advantages of being underestimated for being a kid.
(You'd think after all the Robins the Gotham goons would learn not to, but I suppose they wouldn't be Gotham goons if they did learn from the past)
When Damian is reluctantly included in the more publicized activities like charity galas (bc Bruce does his best to keep all the kids' lives as private as he reasonably can), he is the sevond most angel seeming little terror the Gotham elites have ever been inflicted with, right behind Filemona.
Bruce might pretend to be disappointed, but he is very much enjoying seeing Damian indulge in silly pranks without breaking the serious polite kid act.
(Alfred is very proud and eager to share tips.)
Stray and Damian also share love of all animals and she is his go to buddy to watch nature documentaries with. She is also the person he seeks out when wanting to convince Bruce to let him adopt another animal.
When it comes to Alfred, since he met her as both costumed and her civilian personas without knowing they are one and the same, it's a bit more complicated.
As Kitty, her fake civilian identity, he thought her a charming and polite kid, and was very happy to see Jason make friends with someone outside of the hero community. (Once it was finally revealed she was Stray, Alfred could do nothing but applaud her acting skills)
He did however, as a fellow politely sarcastic individual, recognize the little spark of mischief underneath all the manners.
As Stray, he did find her a little exhausting and her penchant for slightly too catlike behavior a bit much. That doesn't mean he didn't grow to worry or care about her the same way he has about all of his other traumatized, very capable and costumed kids. She's a rascal, but a lovable one, and most importantly, part of the family, even of not officially.
However, after she brought back the kid they thought lost forever and a kid they didn't even know about, as far as Alfred is concerned, she can sit on the fridge as much as she wants.
Stray herself simply loves and appreciates the man as the kinda grandfather figure in her life.