Hi @nihili,
Thanks for trying out /e/ on your device…you did not mention which device you are using.
Let me respond to your queries at least the ones I know answers to 
No not all are Open Source
There is a basic rating system which you can see in the screenshot on this link
There is a long running thread on thishere where users suggest names of apps they want to see in the AppStore
Yes you can install Fdroid. Though I am not sure if disabling AppStore will be a good idea and post that if the ROM will work smoothly. User may be doing this.
Not tested it but you should be able to install it
It is not required for the smooth running of the ROM but some users do root their /e/ phones to install various apps
Not sure which FAQ you are mentioning but if it is this FAQ then the statement has a link which has more details.