When installing my vinyl windows should I put a nail into every little hole around the window? It has a flange that has many little holes around it. Also what size nails would you recommend? Finally do I need to secure the window to the inside of the rough opening, as you do with a door?
Yes put a nail into every hole. I would recommend galvanized nails that are 1 to 2 inches in length. If there is nothing behind the flange but plywood, anything over an inch and the nail will just be sticking through the plywood.
I assume you will hit some framing behind the playwood, so a little longer and you will hit that. I looked over my new vinyl windows in my sunroom and there are no attachment points on the inside of the window.
I don't recall doing anything on the inside of the window when installing. The most important point I remember was with the flashing on the outside. Start at the bottom, then the sides, then the top so that water can be properly channelled away. There is a video below in the comments showing an installation. I remember it was pretty straight forward, just made sure the windows are level.
Yes, I'd recommend putting a nail in every single hole, roughly 1.5 inches in size. I believe what you have are new construction windows because they're equipped with the nailing flange along the outer frame. Typically, vinyl replacement windows don't come attached with this kind of flange for easy installation.
From personal experience, installing a nail in every hole is wasting time and materiel. Most instructions recommend every other hole, which will cover any unlikely warranty issues.
A good resource for this question can be found at This Old House. I find that "This Old House" is a great resource for learning the proper way to accomplish construction tasks. Keep in mind that they do not share any shortcuts...