3) A Commander popped by a Side may have any rank less than or equal to that of the Ruler of the Side. This is randomly determined.
The other option is that it is determined by location. Caesar wasn't popped in the capital, so he is Noble rather than Royal.
4) A Royal or Noble Side may, alternatively, order an Heir to be popped. This Heir will be either a Royal or Noble Warlord, depending on the nature of their side.
4a) Such a Side may pop more than one Heir, who will ascend the throne in order of popping.
I think that the order is determined by the Ruler. However, the unit must have Heir status. This is either due to being popped an Heir, or being promoted to Heir status like Stanley.
5) Any Side without an Heir may pay to raise any Warlord of their Side to the position of Designated Heir.
5a) They cannot do this while an Heir popped as such is living, but they can do this to Designate a different Warlord as Heir.
5b) Royal and Noble Sides generally prefer to only do this with Royal and Noble Warlords who were not popped as Heirs. Example: Tramennis, Caesar. Exception: Stanley.
I don't see why their would be a restriction on promoting units to Heir just because there are other Heirs available, it would potentially be a waste of money though.