I copy and paste my answer from other threads as the content answers the questions you gave - and not gave, but surely have!
The story in the bottom reminds much of Mschauer tells!
"I think it it worth a try.
Shy semiferals are usually submissive to the homecats, and it is more often then not there are no real problems between them.
In fact, this is usually easier then bringing home a new bought homecat... These can fight or be jelaous...
(The exception are not shy semiferals, especielly uncut males. They are often easy to get friendly with people, but they may be nasty to the resident cats beating them up. Thus it is necessary to spay them before you even try to let them meet your residents....And begin with the most docile resident. But this is not in your story... )
If they get pals - they will surely do it if your homecat wants it! - Will make it easier to foster the shy newcomer.
You are also doing quite right taking her first to the vet for check up, shots, deworming. Preferably have her the first two-three weeks in a quarantene, till the shots and deworming are fully working...
Many cat rescuers use their bathroom for quarantene. A big dog crate standing in a suitable place is another alternative.
Good luck and much pleasure with your new little furry friend!
I cut in an answer I wrote earlier. It applies partly to you too.
"Yes. I agree to say the least.
It is astonishing how many semiferals, and even ferals, can be fostered, and also become beloved home pets. Also as grown ups!
We in Sweden have very little TNR. Thus, if the rescuers and cat shelters want to do something with the ferales and semiferales, the practically only option is to take in them and foster, for later adoption.
Of course, the really aggressive arent taken in... Defensive aggressiveness just when catched is something differently and the rescuers can copy with.
They can usually become stricktly indoors cats, as the fosters must kept them inside... Thus, during the fostering time they are inside.
The result?? almost all do get tame and usually good pets too.
Kittens and the sociale are of course easiest. But also the grown ups have a really good chance.
And the ex-homeless are often quite happy to be purely indoor cats.
For a outgoing homecat the outside is a lot of fun and joy. If it gets scary or unpleasant - the cat can always run home. For the homeless it is survival of the fittest. The choice between the terrible world outside to the cosy world inside is usually quite easy. Much more easy compared with a outsidegoing homecat who must become strictly indoors cat.
Our cat forums in Sweden are full of members who witness about their ex homeless, or even ex-ferals, beloved pets. Usually being good friends with the other pets: cats and dogs.
Older very shy ferales are of course more difficult, and take much more time and effort.
I have read an example: the older (6-7 years?) female cat did get somewhat tame, and could live indoor in the house the live of a shy semiferal. Not aggresive to the other cats or humans, but avoiding most contact. But the live WAS saved, the cat was acceptable happy, and the owner had a couple of other cats to pet. So the woman did gladely accepted her extra protegé.
SIX years did it take. Six long years. But in the autumn of her live, also she did become a pet-cat sleeping in the bed with her Mommy.
So. As I understand. It isnt that difficult to get the ferales tame. The difficulty is they dont always become loving pets. And it usually takes time.
If you dont have the time and arent willing to make the effort, it may be wise to put the limited resources on easier cats, instead of a ferale. The sorrowly thruth is there are always cats easier to foster and adopt... There are also many entirely tame, friendly cats seeking new homes"