Hello! I might be able to answer some of your questions but not all of them.
I was admitted out of high school to a "direct admit" program. It's at a four year public university. I spent the first year and a half doing prerequisites, and this spring I will be starting the nursing program. I was directly admitted, so I did not have to apply to the program. However, I did have to maintain a high GPA in my prerequisites.
You cannot become a Nurse Practitioner straight out of high school. You must become a Registered Nurse first, and usually you must have your BSN. I'm sure there are programs that would allow you to become an RN, and then immediately start becoming an NP. However, these programs are rare, and I'm afraid I don't know any. It sounds like you may have found one! But, you cannot just "skip" the RN part, or become an RN and an NP at the same time. In fact, most NP programs require a few years of experience as an RN before you can start their program.
Nursing school is very challenging, and I encourage you to seek more information about being a nurse. I am not an NP, and I'm just focused on getting through nursing school right now :) However, there are many types of NPs. Family NP, Acute Care NP, Neonatal NP, Geriatric NP, Pediatric NP. I could go on and on! It may help to ask about a certain type. A "typical day" in the life of an NP most certainly depends on where they work and what type of NP they are. Also, since there are different types of NPs, there are different colleges to attend depending on what type you want to be. You can't specialize in everything! This website is a great resource. Don't be afraid to use the search function and look at past posts!