Should I Rescue This Cat?

[Placebo]

So a few months ago we started seeing this cat hanging around our building, and we started to leave food out for her, and even made her a little warm bed-type thing, because it was still really cold outside. And when we first noticed her, the second anyone started walking in her direction she would run away terrified...

Fast-forward to today, and she's officially the sweetest little cat ever. I'm guessing she's not fully grown, but I could be wrong. She hangs out right in front of our building all day, and we feed her in the morning and at night just like we do our own cat. She's become extremely affectionate, following us to our car and to our door whenever we leave, and she loves when you pet her; you can even pick her up!

I really want to take her to the vet to get checked up, get her shots, "fixed", etc...

And now, the pictures...



There she is pacing around in the front of our building when I came home from school...



Rubbing up against my leg, aww...



Looking up as if to say, "Please Placebo...take me inside...I love you..."



Eating...



More eating...

GAH! I want her so much! It would take some serious convincing as far as my parents go...and how do you train a stray kitty to use the litterbox? I got nothin'! :)