As far as specialization, depends on the hiring practices of your local hospitals. When I graduated, everyone pretty much was on a level playing field. When you got hired after passing NCLEX, you could go into ER, ICU, OR, Med-Surg, Tele, etc and you completed orientation for that specific area. There were internships basically that were 6-9 months long (most hospitals are only 3 months however).
Some hospitals, especially now, can be more picky. For instance my current facility is applying for magnet and are only hiring BSN prepared new grads. I think they are being more selective in the specialty areas especially and do not hire new grads into some of them, like CVICU. You must have med-surg experience first. Bottom line, depends on the hospital.
As far as vomit, feces - I am the gag QUEEN. But overtime it isn't as bad. I can handle incontinent patients better than dumping a bedside commode for some reason lol. For vomit, try and hold it as far from you as you can and flush quickly. Technically you should measure it though, sometimes I just can't though! Yes you can wear a mask as it's part of personal protection equipment and if someone is vomiting that is a potential exposure. But as was mentioned above, they don't do much for smell.
I have been known to tear an alcohol swab to take a whiff of...also baby powder squirted over smelly things helps mask the smell until you can get it dumped.
There are areas of nursing with less exposure to these things. If you work more with ambulatory patients who can do their own toileting for instance. Procedural areas have to deal with it less than say med-surg. Med-surg would have to deal with it less than ICU because they have CNAs who do most of the toileting.
It was funny a few weeks ago I was working ICU and had a pt that had diarrhea like 6x during my shift. His son was helping me and I noticed him gagging and turning his head away so after that I got another staff member to help me. But for me, I didn't even notice the smell at all! I thought WOW I have finally gotten used to this! lol