CNA/ PCT/ Hiring Questions

These may be silly/common sense questions, but I am kind of confused! Sorry if these answers can be found somewhere else on the site; I did a search but was having problems deciphering everything!

So I was hoping to get into a PCT program but the waiting list was too long. I needed to get into a class ASAP to start working. I am now in a CNA class that will end in about a month. I really would love to work at a hospital as a PCT, but I will only have my CNA. Has anyone personally been hired and then trained in the additional skills, such as EKG and phlebotomy? Did you already have CNA experience?

And I am unsure of the best way to go about applying to a hospital. I have seen different suggestions on here. I see openings listed on their website, but I hear they may not be actual openings, just expected ones. Is it best to actually send in my resume/cover letter or to apply to the jobs online? Or should I actually call HR prior to placing my application? Or after? As you can see, I am not familiar with the hospital hiring process and any information would be very much appreciated!