IP design: master and slave
Yes, I think that all your comments are correct.
A master requests data (or sends data) to the slaves.

A slave cannot originate a bus transaction. It must wait until the master communicates to it. In a bus with many slaves, the master can communicate with all of them but the slaves cannot communicate between them.

For many cases, this is just OK since the slaves don't even know of the existence of other slaves. When slaves have to communicate between them, usually a mailbox system is implemented where a slave that wants to communicate to other slave indicates this to the master. But it cannot originate transactions on the bus.