How to estimate the area required by first responders with a stretcher?
There is no code requirement for width of hallways in residences.

However, the minimum width for hospitals is 6’. This is primarily so gurneys can pass. (Btw, ER gurneys are much bigger than ambulance gurneys.) 

The commercial code (not residential houses) require a doorway to be a minimum of 32” clear opening when the door is in the “open” position. If you add 2” for the door to project into the clear opening AND add 1/2” on each side of the doorway for the “stop”, then the minimum width door is 35” wide, but 36” is a standard width and makes it slightly easier for the wheelchair to pass through the doorway. 

When we layout bedrooms, we leave about 2’ from the bed to the wall. This is for a nightstand and for ease of making the bed...which I think would be good for the caretaker too. 

Also, remember that EMT’s get people out of bathrooms, etc. so they’ll get them in an emergency.