Whenever Mogget's collar is removed, Mogget exhibits a maniacal desire to exact a blood price from the Abhorsen. At first glance, it appears that since his collar has been removed, Mogget is now exhibiting his true self.
However, it's not so. The Seven didn't just create the collar to bind Yrael to the Abhorsen's service as Mogget, they naturally also applied more mundane Charter Magic to corral the Free Magic in him (much like the spells that suppressed the Free Magic in Clariel and Nick). But they left one aspect of Mogget's Free Magic personna uncorralled: his desire for vengeance. This is normally only a small aspect of Mogget's personality, but because it is left unsuppressed, it's the part that manifests when Mogget's collar is removed. And the Seven did this for a very specific reason.
Being a Bright Shiner, Mogget is a very powerful Free Magic being, and the Seven knew the Abhorsens would occasionally need to make use of Mogget's powerful Free Magic as a last resort. But the problem with doing that is, Mogget must be unbound before he can use Free Magic, and once that happens he would be free and no longer have to serve the Abhorsens. So the Seven devised a way to ensure that Mogget would always return to the Abhorsens: they made it so that he would desire revenge whenever released. Not only that, but it seems as if Mogget needs to make sure the Abhorsen is aware they are paying the blood price. Given that's it pitifully easy for an aware Abhorsen to bind Mogget again, it gives the Abhorsens the ability to exploit Mogget's Free Magic powers relatively safely, and without having to worry about getting Mogget back.
Mogget, for his part, seems to be under no illusions about this. He advised Sabriel to remember the ring before she removed his collar, and, after he became FreeMagic!Mogget, he said he only had to make Sabriel pay the blood price before he was free.
Basically, it's just another binding on him, a clever one that (unlike the collar) works even while allowing him Free Magic power.
Prince Sameth was somehow born as a Wallmaker even though they had disappeared from the Old Kingdom centuries ago. How? Simple, he got it from his grandmother. Although Wallmakers had disappeared from the Old Kingdom, some old Wallmaker blood was still kicking around Ancelstierre. Elinor's Clayr gradmother probably had a vision about marrying someone in Ancelstierre for their Wallmaker blood, seeing as how Orannis was starting to show signs of breaking out of its bonds, and Charter knew they'd need a Wallmaker to bind it again.
We might observe that being an actor could be a good way for Elinor's Wallmaker blood to manifest itself growing up in an area separated from the Charter. Acting is, in many ways, about creating something new.
