This feature is available on all Goodshuffle Pro Plans.
Yes! Anyone who is added as an additional recipient will be included in all messages for that thread.
You can have multiple different threads on the same project - said another way, you can have one message thread with just your Client, and another with the Client and their accounting department or wedding planner. These threads will act independently - clients added to thread A but not thread B will only receive messages in thread A.
Below is an example of multiple threads for the same project.