Some yes, some no. And it's a surprisingly-even split.
There's no general rule on undead: either the Frightened condition (PHB Appendix A) or the Monster Manual's section on undead (MM pp.6-7, "Types") would be the places to look. But each specific undead's stat-block describes whether it is immune to the Frightened condition. (Is there any reason to why the list of undead that can be frightened seems counter intuitive? addresses the "why" of this.)
For reference, the MM has the following Undead which...
cannot be frightened:
Banshee, Death Knight, various Liches, Flameskull, Ghost, Mummy and Mummy Lord, Revenant, and Shadow.
can be frightened:
Death Tyrant, Crawling Claw, Ghast, Ghoul, Bone Naga, various Skeletons, Specter, Wight, Will-o'-Wisp, Wraith, and various Zombies.
This GM would have the humanoid type effectively replace the corporeal creature's undead type with regard to that undead bloodline sorcerer's mind-affecting spells
Although it's possible to read the two sentences of the sorcerer's undead bloodline bloodline arcana in isolation, I disagree that a reader should. When the description says, "Some undead are susceptible to your mind-affecting spells," the reader also needs to know which undead and in what way such undead are susceptible, and those're covered by the second sentence. To clarify with brackets, that second sentence should probably be as follows: "Corporeal undead that were once humanoids are treated as humanoids for the purposes of determining which [of your mind-affecting] spells affect them."
Thus this GM would rule that when that undead bloodline sorcerer casts a spell that does not possess the descriptor mind-affecting, that spell is wholly unaffected by the bloodline arcana. For example, although each spell normally targets humanoids, because the spells are not also mind-affecting, the bloodline arcana would not allow a sorcerer to make bigger with an enlarge person spell a once-humanoid zombie, paralyze ironically with the spell ghoul's touch a once-humanoid ghoul, or shrivel with the spell wither limb a wight's leg. In short, it seems to this GM that if the sorcerer's spell is not mind-affecting, then the spell's effect is unchanged.
However, when that undead bloodline sorcerer casts a spell that possesses the descriptor mind-affecting, this GM would treat any once-humanoid corporeal creature that possesses the type undead as possessing, instead, the type humanoid for the all the spell's purposes, and that humanoid type would determine all the spell's effect. Thus, at its most basic, in this GM's campaigns, such a sorcerer could befriend with a charm person spell a once-humanoid ghast, send off to slumberland with the spell sleep a group of once-humanoid skeletons, and exercise mental control using the spell dominate person over a once-human and extraordinarily unlucky lich.
Further, because this GM would have the creature's undead type effectively yet completely replaced by the humanoid type with regard to the sorcerer's mind-affecting spells, the once-humanoid undead creature would likewise lose any of its immunities and resistances due to its type against that sorcerer's mind-affecting spells. For example, a once-humanoid mummy could be stunned by the sorcerer's color spray spell, despite undead creatures normally being immune to the condition stunned, and a once-humanoid vampire would be dealt Strength ability damage and be stunned after succeeding on the saving throw against the sorcerer's weird spell, despite normally being immune to all three of effects that require a Fortitude saving throw unless the effect also affects objects and damage to its physical ability scores and the condition stunned.
This can lead to some unusual situations, like a once-human corporeal undead creature believing it's been poisoned after failing its saving throw against the spell illusory poison even though it's normally immune to poison, or a once-human corporeal undead creature believing it's suffocating after failing its saving throw against the spell phantasmal asphyxiation even though it doesn't breathe. This GM, though, sees such unusual (and not to mention amusing) effects as features rather than bugs and suspects that any sorcerer that'd pick the undead bloodline would also. In fact, I suspect such a sorcerer would pick to know such spells deliberately so that he could revel in his undead brethren's strange, normally-impossible discomfort!
Best Answer
Two of the three creatures you listed as being immune to the frightened condition have abilities that can give that condition to others, while none of the creatures listed as susceptible do.
It makes sense that creatures capable of frightening others would be impossible to frighten.
However, this does not account for the shadow.
After further examination, this pattern seems to hold true for all the undead in the SRD. Creatures with immunity to being frightened tend to have the ability to frighten, while those without never do.