I am only a 4th year med student who rotated through the NICU this year, so my thoughts maybe are not the most accurate, but they will give you a general idea nonetheless.
How competitive are the fellowships for neonatal? NICU is a fellowships in peds that has among the most positions per year. Therefore, getting any fellowship is relatively easy as long as you do well in residency from an average program. To get a fellowship at one of the best programs in the country is attainable but much more difficult, and if you want to be at a top-tier program (the top 10 in child magazine include CHOP, Rainbow Babies, Emory, Riley in Indianapolis, Baylor, Boston Children's, Milwaukee, Denver, Columbia, and USC) then you it would behoove you to go to a very good residency program and work hard.
What is a typical work week/month like? This depends if you are private or academics. In private practice, typically you are on service in the NICU several months a year and have pretty frequent call, unless you are in a very big practice. Academics tends to be better lifestyle with being on service in the unit 4-8 months per year with research time the other months and taking overnight call less frequently.
What happens in a typical day? The typical day again depends on how acute of a NICU you work in. In a level III NICU you will have the sickest babies and have a lot more issues to deal with since the babies typically are less stable and have more complex issues such as severe prematurity (eg, 23-30 weeks), complex heart disease, necrotizing enterocolitis, diaphragmatic hernias, abdominal wall defects, neuro issues, etc. In a level II NICU, the kids generally are healthier and dealing with less severe issues like feeding and growing, mild prematurity (eg, 30-37 weeks), etc.
What types of procedures do u do? Placement of catheters in the umbilical veins and arteries, intubations, lumbar punctures, chest tube placement are the things I did as a student. There may be others as well.
Is it more stressful than most fields? It depends on how you look at it. Most of the attendings are pretty laid back and do not get too stressed out. I would say it is no more stressful than other peds specialties with pretty sick patients, such as PICU, heme-onc, cardiology, etc.
How can I get experience/research in this fields before MSI, or after? If you go to a medical school with a decent sized children's hospital, research will probably be going on in the NICU. If their are NICU fellows, there will definately be some sort of research going on. I would simply write an email to one of the attendings and introduce yourself and your interest in research. I am sure most of them would absolutely love an eager medical student to help out.
What is a typical salary? Very wide range depending on academics vs private practice. I believe
www.salary.com will have information about the average salary of a neonatoligst in your desired geographical area.