Nothing to add to what our resident Dear And Glorious Physician wrote, except that he missed your last question:
Generally speaking, you shouldn't have to worry all that much about helping an injured person who is bleeding. Yes, there are technical, theoretical and hypothetical risks in doing such a thing, but for the most part... you would be very much unlikely to catch a disease at an accident scene. We could get into every possible scenario here, but (again)... we've done that kind of thing before.
I would suggest, however, that in such a rare instance as being presented with an injured citizen before professional help arrives, the best course of action is to do NOTHING AT ALL except call 911. It's not a good idea to move an injured party. Generally it is recommended that you can and should keep the person calm, talk to them, and say reassuring words of encouragement. Heroics are rarely necessary. In extreme situations, go with your gut. If someone is bleeding profusely and you think it may be life threatening, apply direct and firm pressure with whatever type of cloth is available. You'd take off your shirt or get a towel out of your car (you should always carry a towel) or whatever. Tourniquets are often not necessary and can be dangerous if applied by a non-professional or someone untrained in first aid.
And also... you can simply carry some latex gloves in your car with you, just for the hell of it. They come in handy if you have to change a tire on your way to a meeting where greasy fingernails would be inappropriate. I used to keep gloves in my vehicle so I could pick up trash on the beach (different kind of Good Samaritan stuff). I suppose I should get some more.
It would also be a good idea to avoid getting blood in your eyes, but I think this pretty much speaks for itself.
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