I'm going into hospital and im being put to sleep by anesthetic being injected into my IV does it hurt?

Very little. Any intravenous medication can sting or burn a little as it is administered, particularly one of the main IV anesthetics called Propofol which does burn a little. However, most patients are given some sedative medication prior to proceeding to the operating room to make the experience more tolerable, and may patients don't even remember receiving the IV medication to put them to sleep.
Maybe for a few sec. Our "induction" drugs Propofol and etomidate both may sting when administered. We try adding Lidocaine to help with this. This is why they found Lidocaine with michael jackson. Maybe 30-50% feel it. I've felt the sting with my surgery...It goes away in a few seconds. Not fun, but nothing i'd lose sleep over -literally.
No. You will get multiple different drug to "go to sleep". They will not hurt.
Yes and No. Intravenous or IV anesthetics may cause irritation of the peripheral veins. An example is Propofol or diprivan. Your anesthesiologist can prevent the hurt by giving intravenous local anesthetic like xylocaine (lidocaine) or mixing it with the Propofol before administration of the drug.
Sometimes. When being placed under general anesthesia, there are many different methods; IV induction is very common. Further, there are numerous different medications that may be chosen by your physician, he or she will choose the one that is most appropriate for you in your situation. A very common agent is propofol, this agent, more than others, can be associated with discomfort on injection.