Function apps sharing Storage

We have an azure Function app (Function_A), and now we want to migrate Function_A to another ASE. We don't want any downtime or data loss so we will create a Function_B in the new ASE using the same storage as Function_A, and running with the same code/configuration.
When both Function_A and Function_B are running, Could all the non-http triggers be triggered only in one function app?
e.g.:
1. TimerTrigger : Seems we need to set the same host ID in these two functions to make TimerTrigger only run in one app?
2. CosmosDBTrigger : Yes.
3. QueueTrigger: Yes.
4. EventHubTrigger : Will Function_A and Function_B both consume the data in the same eventhub?

When we are shutting down Function_A, will it wait all the current running tasks to complete before shutdown?