How to start a process chain from the shell

Question

Is it possible and if so how do I:

1. Start a /bin/bash process that is not bound to a terminal from a terminal? Hence, a shell process that shows up in the process tree as init -- bash. (Shells usually have the process tree structure terminal-emulator-of-your-choosing -- bash)
2. Start a /bin/bash process not bound to a terminal that has as its child another process e.g. a browser like firefox from a shell session in a terminal? Hence, a shell process with a child that shows up in the process tree as init -- bash -- firefox.
3. It is easy to get init -- firefox directly from the shell via something along the lines of exec firefox & exit or /bin/bash -c firefox & exit.

(This question is part of a series of related questions that first enabled me to formulate these questions precisely (cf. How to "correctly" start an application from a shell and Is reparenting from the shell possible?). The three questions have been formulated and discussed partially in the comments of the two former questions but as I see it not been answered. Furthermore, they do seem more appropriate as short question in their own right not suited for discussion in comments.)