Hello
You are jumping a lot of releases and although it should work there are a couple of things that have changed so you should make sure you are not using them (ex: the console.systemModelRenderer.maintainBackwardCompatibilityInSystemId flag, or agentZooKeeper variale in glu script, etc...)
To answer your questions:
1. I believe it should work and you should definitely take it slow. I would recommend backing up the console database. Then switching the console to 5.6.1. If everything works, then switch 1 agent to 5.6.1. If it works then switch 2 agents, etc... until you are confident and can switch everything
2. No there are not been major changes. Only a couple of features were added and it is backward compatible. But definitely run some tests before you go full blown
3. The console is only reading the state in ZooKeeper. So changing the console has no effect for ZooKeeper. Every time you stop/start and agent it will write its state to ZooKeeper and the console will pick it up.
Note that you should be able to use the agent upgrade feature built in the console...
Yan