And what happens when a regular subgeneral gets a 1 PIP dice with an Inert C-in-C? Can he still have its free PIP?
I say yes.
I would say no because an Inert deduct 1 PIP to all his subordinates and this means that this command will have 0 PIP.
Yes, if the sub-general is assigned 1 PIP, that gets reduced to 0.
The free PIP for regulars must be substracted from those available...
Where does it say that? I read the rules to say that that the "free PIP" is subtracted from the cost of the move, not from the PIPs available ("1 less PIP is expended...")
...so you cannot substract something from zero.
Irrelevant, see above.
Is this correct?
I don't think so.
Firstly, there's nothing I can see in the rules which says you have to have a PIP to spend in the first place. Rather, what you do is calculate the cost of each move in PIPs. For example, if you want to move a group of regulars with a sub-general straight forward at full speed in open terrain, the cost is 1 PIP (Each tactical move by a group) minus 1 PIP (one move by a regular group containing a sub-general) equalling 0 PIPs. Having calculated the cost (in this case 0 PIPs) you then move the group. I don't see anything in the rules which says or implies you have to spend a PIP first, and then get it refunded because of the general's presence.
Secondly, there are moves which cost 0 PIPs already - first march entirely along a road, first march by pike group, first march move by naval in good going. So the idea of a move which has an initial cost of 0 PIPs is established. As far as I'm concerned, if a command nominally has 0 PIPs, it can still move its naval group once, move some troops along a road once, and move a Pk group once.