Definitely study more on object oriented programming (OOP). If I was doing this project, I would use classes to describe the RPG characters and store status info. There are a lot of good tutorials online. Try checking out this page as a basic overview: http://www.cplusplus.com/doc/tutorial/classes/ . There are many ways to use OOP in your program, so do some research before you jump right into coding.
Yep, make separate classes for each type of enemy and the player. Then add functions for attacks within those classes and then make a completely different function where the player takes damage (say if you have armour it may affect the real damage)
Also you should learn about vectors, they come in handy, eventually.
I'm stumped. If I have separate classes for each type of enemy, is there a way to call them based on a variable? The majority of fights would be random encounters, and I think it would get excessive using IF statements for each enemy to call each class and its objects.