There are no specific moments when new med ninja apps have to be opened. It's simply the head of the Hospital who decides whether we should have new apps or not.
Actually I was told by one of the mods when I first joined that you can recieve Med jutsu training at any rank. unless this has changed. still thank you for the info.
There are no official requirements as far as I know, meaning that Vincent, the head of the hospital, can pretty much decide on whatever requirements he sees fit when he has new apps. Though logically a higher rank means that you should have more RP experience (in the least the potential to learn more). The chance that a genin ever will be chosen is almost zero. Not to mention you need to take into consideration the basic rule about what kind of rank of jutsu you can use at which ninja rank. A chunin can't learn A-ranked med ninjutsu, making it not very useful to make such a person a med ninja. Finally, as med apps are very rare and strongly desired by much RPers, many experienced and high-ranking RPers will probably apply.