Do Medevac aircraft need to maneuver within stricter maneuvering/ attitude limits to ensure the safety of the patient? Or are there recommended operating practices?
Ie:
That would depend on the nature of the emergency and the health of the patient.
For example I know someone with severely reduced lung function, she can't fly at normal cruise altitudes for commercial aircraft because the cabin air would be too thin for her to survive, so when she flies (medevac only these days, obviously, or light aircraft or helicopters) the aircraft must stay below 10.000ft. For someone being evacuated with just a broken leg that'd not be relevant (most evacuation flights here are of that nature, returning people with injuries related to ski accidents home for recuperation).
Medevac flights, like all commercial flights, tend to avoid violent maneouvers anyway, for comfort and to reduce structural stress on the aircraft. They also try to avoid inclement weather for the same reasons (normal aviation safety). All of that covers pretty much everything in your list already for any commercially operated aircraft, not just medical flights.
Obviously for military evacuation flights out of combat zones all that goes out the window at least until you're out of reach of enemy ground fire, and to a degree that might also be the case if the medevac helicopter or aircraft has to land in unusual spaces where some unusual maneouvers would be needed to get in and out of there (this might even affect some hospital helipads, not all hospitals were built with them in mind and retrofitting them sometimes left them in tricky spots).
