The transporter AI would know about the orange car, but it doesn't know it's not supposed to be there. Let's change grey bricks to, let's say , Ensign Picard. He's waiting for his first assignment with his pals. He gets into a fight with some Nausicaans. He has to have his heart replaced with an artificial one (the orange police car). His next transport can't remove the piece that it thinks shouldn't be there. Each person would have to have a file of "what they're made of" But that would preclude beaming someone up (or down) from a new world.
As to the second point, technically they can do that (Tasha), but one, that may have been decided that it is unethical and is not allowed. Other wise, it could be done, but just isn't. I was writing a script for TNG when it was on where upon beam up, a crew member was hit by lightning at dematerialization. The surge was partially brought up and went thru the system. The damaged transporter lost the pattern but pulled part from a program that was just being shut down in the holodeck but used still had the crew members conscience. (I forget the details, but I had it explained better in the script). So the dilemma of the story was who was this person (way before Tuvix)? Was it Ensign So-and-So or K'Ehleyr (Worf was finishing up her death anniversary in the holodeck). I'm not presenting it here like I wrote it out, and I never finished it because TNG ended. I have it on a harddrive somewhere.
(this was written because I wanted to bring K'Ehleyr back

)