This is how i've seen the rules interpreted--
Indirect kicks that are played forward are called just like "run-of-play" offsides calls. A "touch-and-shot" indirect kick is more like a direct kick.
Offsides on a direct kick is as follows: if the shot is on frame (or otherwise deemed a shot) and a player is in an off-side position but does not influence the play, then there is a delayed off-side or advantage call. If the player is is an off-side position and influences the play, then the off-side is called.
Realistically, the only indirect inside the box should be a pass back. The aforementioned parameters apply. Also, any foul deemed a direct kick inside the box should result in a penalty kick.
Keep in mind, these are only the ways i understand the rules and have seen the rules applied and interpreted. I would welcome a post from a certified referee.