When I used to sell blood and plasma, the more shitty phlebotomists would miss the vein and scrape the bone, or go all the way through the vein (hematoma). I had a doctor snap off a regular needle in my ass, and have to pull it out with those pliers thingie.

No, but if they don't aspirate the needle, they might inject it into a blood vein.

Yes

they would have to jab you really hard then bend it for that to happen. extremely unlikely unless they did it on purpose