The App only allows a single phone to be connected now which is a problem when both me and my wife want access.
Polar opposite of our experience. We have two Nest thermostats in our home and both my wife and I can connect to and manage each one with our respective phones.
There is also no way to run the fans without switching it on heat or cool.
Also not our experience. We can run the fans independently of heat/cool. That could be a consequence of your HVAC system opposed to the Nest itself.