THE SHORT ANSWER:
These two are great questions. I agree with the people in part I who suggest telling them, "I'm sorry, but I don't discuss religion at work."
I wouldn't cite hospital policy unless there is one, because you might get in trouble for lying if there isn't.
A lot of people will leave it at that. But, for part II, what if they don't?
You can suggest to them that if they feel a strong need to discuss their religion, you can refer them to the hospital chaplain. That's what he/she is for.
If they push further, you can add, "I'm sorry. I need to focus my attention on this chart/blood draw/whatever."
THE LONG ANSWER
The problem, however, is that the pushy people who "witness" this way don't really do it to help others. They're doing it to prop up a weak ego.
Forcing you to listen against your will (you're held captive while you're with them and can't simply walk away) isn't about religion. It's about being in control. That control isn't necessarily about converting you. It's simply about forcing you to listen or hooking you into a debate.
Of course, they won't see this (and neither will some other people on this forum who are like that). Their egos convince them that what they're doing is what they're supposed to be doing, and they remain unconcerned about the wants or needs of others.
But I think the most important thing you can do is remember that none of this is about you, and you can't genuinely make their hospital experience better if their primary goal is to witness rather than to received medical care.
I don't agree with the person here who said it's your job to let them say or do anything, because they're the patient. Witnessing to someone is not the same as talking about your grandchildren. Trying to force your views on someone is rude in any setting—if it weren't, there would be no reason why you couldn't force pantheism on this patient in return.
Your experience at the hospital matters, too. What if the patient were a man who kept grabbing your @ss. Would you just let him go ahead and do that, because hey, it's HIS experience, and he should get to do whatever he wants? Let's let him raid the morphine while we're at it!
No. There are limits to what patients may or may not do. If a patient became rude or unruly along other lines, you would have recourse through the hospital—I doubt they would ask you to "just let them do it—it makes their experience better."
So I would actually check into your hospital policy, because there may be rules that exist to protect you, too—from being subjected to rude patients, and this qualifies. It's not your job to be subjected to any kind of hostility, and once you've expressed that you're not interested, it's hostile for someone to force you to continue. No means no.
p.s. Discussing religion (or anything) is not the same thing as forcing another person to listen to you speak. A discussion is voluntary—you can opt out.