Yeah you really did not introduce them the right way. You should start over and do it properly, but first you should take him to the vet to get checked for contagious diseases that can be fatal to cats as you would not want to spread it to yours. They can also check for a microchip in case he is a lost pet.

After that, you need to set aside a room that is not important or favoured by your cat Anya, and designate that as his room. You should also give Anya a space where he is not allowed to go at all so she feels she has a safe space from the intruder. Here is some instructions how to do this properly, it may take weeks or longer for them both to be comfortable:

https://spca.bc.ca/faqs/how-introduce-new-cat-old-cat/

There are lots of similar instructions available. But you always start with them separate, then bring them something with the scent of the other one like a blanket (not pee or litterbox), then allow brief visual contact with a barrier, allow them to explore eachothers space when the other one is confined somewhere else, and then allow them to meet and interact while supervised, then allow them to interact unsupervised. Each stage can take anywhere from hours to weeks, but you cannot proceed to the next step until they are both completely comfortable. Cats are easily stressed at times and can stop eating or peeing and this can cause serious harm to their health or even be fatal.

I’m sure with some calibrating you could just cut off 1/3 of the edible portion. While the core-containing portions would be heavier, the edible apple weight would be the same. It wouldn’t be easy to do first try though

In one slice, cut a third off of each apple, and you’re left with 3 portions of 2/3 an apple each

It could also make a fun sound

Can you be more specific about what you feel should be changed?

Feline hyperesthesia is probably what you’re referring to with her tail self-mutilation. Definitely odd there would be a random residual infectious tick in a new house lol, but stranger things have happened! Weird !

What ended up being wrong with her?

Weird, but they don’t think he injured himself?