Knowledge checks and creature weaknesses

[Nikos Kakavoulis Papadimitriou]

Hello people, we have a small problem in my gaming group, so I require your assistance.
I just played my first session in Pathfinder, role-playing a smartass witch with loads of ranks into knowledge skills. We encountered a Babau today, and I succeeded in my Knowledge (the Planes) skill check (I specifically asked the DM whether I knew which was the Babau's lowest save, so that I could use the appropriate spell on it).
The Knowledge skill reads 'Identify a monster's abilities and weaknesses, DC = 10 + monster's CR.', so no definitive answer there. The description of the Babau in the pfsrd reads: 'DC result 16 ...This result reveals all outsider and tanar'ri traits. Now, the outsider traits are darkvision, weapon and armor proficiencies, blah blah blah.. while the outsider FEATURES list 'two good saving throws, usually reflex and will', so the DM told me its traits and argued that the creature's saves (I wasn't even requesting for the specific numbers, just which is the worst one) aren't traits, but features, so I couldn't have known them.
I threw a considerate amount of ranks in Knowledge skills so that I would identify the adversaries' weaknesses, but my DM considers saves a trivial knowledge and not a common one.

So I have two specific questions:
1) Can I identify a creature's lowest save with a Knowledge check equal to 10 + said creature's CR? If not, then what would be the Knowledge DC for such a piece of knowledge?

2) When I succeed on a knowledge check and the creature type's traits are revealed, do I know its features as well (knowing a creature has a high Will save would lead me to target either its Fortitude or its Reflex save with a spell, for example)?

Please help out a fellow player, for me and my DM are kinda rivals and it would greatly help settle the score (and such knowledge would greatly help the party.
Thanks in advance!

[Starglim]

When you make the DC for monster knowledge, but not higher, you know what sort of monster it is and get one piece of useful information. The GM can decide what to give you (the PFSRD doesn't have the text you mention, nor for the Knowledge skills, d20PFSRD sidebar is marked as Fan Content and is from a 3.5 source that gives incorrect information for Pathfinder). To me, identifying a creature includes its name (unless unique), type, subtypes and all abilities granted by those categories, though for practical time management and general policy I wouldn't like players to flip through the Bestiary while combat is running. I'd also give the creature's best-known or most obvious special ability.

If you made the monster knowledge DC + 5 or higher, I'd take questions, such as the creature's lowest save (as opposed to that of its type).