How does adding Inquisitors to an army work, and can they form their own army?
Adding Inquisitors to an army works in one of two ways, according to this Goonhammer article:


If you have an inquisition detachment, you can only include one INQUISITOR. This is presumably intended to make a detachment represent a single Inquisitor and their retinue.
If your army has no INQUISITION detachments and every unit in your army is either IMPERIUM (excluding FALLEN) or UNALIGNED you can add a single INQUISITOR unit to any other detachment without using up a detachment slot. This does not prevent that detachment from benefiting from abilities like Chapter Tactics, and also doesn’t prevent your army benefiting from abilities requiring your whole army to share it (like the most important example, Combat Doctrines).


So you can either add an Inquisition detachment with only one Inquisitor, OR add a single Inquisitor to any number of your existing detachments.