Name, type, keywords is dc 10.
Powers is dc 15. Notice: Powers does not tell you only that kobolds have shifty, but also that a wyrmpriest can fire blasts of energy at you based on its dragon's element. That's class based stuff, right there.
Exactly how does the monster know which powers the PC took?
'Hmmm, that stance he is using indicates that he makes short stabs with that sword, however his legs are poised to make a wide sweep with the blade. Watch out for that.'
'I smell marjorum and bat-poo. Prepare for a fireball.'
'Look. He has a bow, and two arrows knocked. Maybe he's gonna fire both at once.'
Narratively speaking, it's certainly not implausible.
How does the Arcana check against the PC Eladrin Cleric (arcana since it is a fey creature) tell the monster about Clerical powers?
'Eladrin society includes a sect of priests to Correlon. The warriors carry weapons which are lit with the light of Correlon himself, meanwhile he gifts others of this order with the luminance, and thusly they fire it directly.'
How does the monster even know that it is a Cleric with an Arcana check? Maybe it's an Invoker.
'Look. Divine magic pervades him, but he bears no symbol of the gods. He must be channeling divine power directly! Look out, Scrug, this guy carries the wrath of the gods in him!'
Monster Knowledge checks are not there for the convenience of the PCs, they are there for the convenience of the players. And they are not there for the convenience of the monsters.
Poppycock. That's like saying monsters can't Stealth or climb stuff.
They are there so that the player has a rough idea of the universe of the PCs.
And the NPCs would -not- be aware of this universe? I guarantee you that an ancient red dragon (as an example) isn't exactly a newbie in this universe.
And what if said monster is Vecna? I -assure- you Vecna probably has a better idea of the differences (for example) between Invokers and Clerics and Avengers. Probably even more than Invokers, Clerics, and Avengers themselves.
Scale down as level-appropriate.
Nature and Arcane checks tell one about racial capabilities, not class capabilities.
Incorrect.
In the case of monsters, their powers are racial. In the case of PCs, their class powers are class, only their racial powers are racial.
Incorrect. Monsters don't have racial powers, every power is unique to that monster. It's only for convenience sake (and grokkable design) that monsters of the same race share a power or two.
Human PCs can have thousands of combinations of different class powers. A single nature check should not tell a monster exactly which powers out of those a human is capable of using until the power affects the monster. That is why there is a "monster knows what affects it" rule.
Monsters can have -more- combinations of powers than humans can. Human PCs are restricted to powers of classes, monsters can literally have -anything.- Monster knowledge checks give you information on monsters not yet printed. If arcana gives you knowledge of elf society, then it gives you information on elven military techniques (warlord stuff), elven magical schools (wizard stuff), and elven spirit-worship (shaman stuff)
PCs are diverse creatures with thousands of possible capabilities. Monsters are specific creatures with set powers. Even if used, the DC for figuring out what a PC is capable of should be very high.
Monsters are not specific creatures with set powers. A kobold slyblade is a totally different animal than a kobold dragonshield. And a DM can mix/match powers, and change things up, and still the PC could figure stuff out...
So yes, a successful knowledge check will tell a monster that a Halfling has the Second Chance racial power, but it won't tell anything about class powers. How can it? What does a Nature check have to do with Warlock powers or Wizard powers or Rogue powers? Those are outside the realm of that skill.
So, a PC Human Wizard can use a knowledge check to figure out that a Human Mage has Magic Missile, but that -same mage- can't use HIS knowledge check to figure out that the Wizard also has Magic Missile?
Or... that an NPC Eladrin Wizard with Magic Missile and Flaming Sphere trained in Arcana can't use his skill to discover that the Eladrin Wizard in the party with Magic Missile and Flaming Sphere doesn't have Magic Missle or Flaming Sphere, but the Eladrin Wizard in the party -can-?
I'm sorry. That doesn't even -make sense.- Monsters are not necessarily ignorant about the world they live in, for -the same reason- that PCs aren't. if they -have- the skill, they can -use- the skill. That's fair play.