I can offer some insight only for a couple of points:
- Rooms are not supported natively, but there is a plugin available (GitHub - MitjaNemec/ReplicateLayout) which I am the author of. As I am not familiar with the Altium’s room functionality I can not say how they compare, but the plugin is quite versatile as it allows for source and destination room to be on different layer (top/bottom) and it properly handles nested rooms. The terminology is obviously different and I think that the worst part of it is the practically nonexistent documentation.
- There is currently no way to bind the plugins to keyboard actions. You can change the shortcuts, but I can’t tell if existent flexibility will allow you to come near your Altium experience.