First and foremost, I have to say that I am in love with Medical Edge. I've been spending a lot of time on it lately because I enjoy studying medicine and also because I am starting to do research for my novel. It's set in 1939 through to 1943. I have three questions for you.
Nursing in your time frame of 1939-1943 would have looked a lot different than it does today. They definitely wore uniforms and caps. Doctors would have been formally called "Dr. Smith" versus using first names like we do now (although not in front of patients).
Nursing work was viewed as inferior to the physician meaning—you do what the physician says. Now, a nurse’s input is more respected. Doctors and nurses realize they can't work separate from one another.
Nurses likely didn't specialize then like we do now and there was likely not a lot of physician specialties either as there weren't any intensive care units or emergency departments until the 1970s. Equipment would have been non-existent like the heart monitors and stuff we now use. Read through this info to get a general feel of how the floors or "wards" would have been split up.
This link is from Britain but would probably have some cross-over to the US. Here is a link to some personalized stories from people who nursed during your time frame. I would read through these for the 1930's and 1940's to get a feel for what their jobs were like.
Another one of my main characters goes off to fight in the war. How severe would an injury have to be for him to be discharged? Presently, I have a situation designed where he is aiding a family out of a bomb shelter; there is an unexploded shell nearby, and a child accidentally kicks rubble at it and sets it off. Big boom, main character loses part of his leg and half of his body is burnt. I'm also thinking that he loses his hearing. Would this be plausible?
I would search military discharge related to a medical condition two ways. One—what medical conditions are prohibitive for military service and those conditions that would lead to discharge.
I found this list, but you could probably find more and if it's the 1939-1942 time frame it may be different than those that cause discharge in these times.
The injuries you list related to the bomb blast are realistic and I think would be enough to cause his discharge from the military as well.
Lastly, my nurse has a patient, a woman in her 40s or 50s, who she loves with all her heart. I want this patient to die. What would be a good way to kill this woman off? I need her to have been in the hospital for around four years. I also want to have her weak but able to speak with my other characters. What's a good malady for this situation?
These diseases fall on a spectrum (more MS and the autoimmune diseases) but Lou Gehrig's Disease and Huntington's Chorea lead to neuromuscular wasting, etc that does lead to death and there is currently no cure.
In that time frame you're looking at you'd have to determine if they were able to diagnose these diseases. To do that you could Google search "When was Lou Gehrig's Disease discovered?" That should get you in the ballpark to know if the medical community knew about whatever disease you chose for your time frame.
Keep in mind—it would be highly unusual for someone to be hospitalized for four years straight.