Sorry if I couldn't deliver a much...swifter answer, but I had to ponder on the new approach to answer.
Lethargy seems like the odd one out there, stronger than the rest, but there's two reasons for it. One is because it deals with skirmishers specifically: those who move and attack. Be it the inefficient Spring Attack, the more efficient Fly-By Attack, strafing maneuvers, Skirmish, amongst others, this is meant to be the aura against them. However, there's another use for Lethargy, one that needs yet another approach to use it. And afterwards, an explanation on mechanics.
The second tactic is, effectively, lockdown. Having a character pretty much pinned to the ground does wonders for preventing perimeter breach, since it forces the character to either teleport or resort to less effective attacks, barring having the Bez-Kismet stand there and get all the pummeling (which it can resist, what with having d10 and strong AC). It's sort of the same lockdown provided by trippers, but far more potent and easier to counter.
Now, the difficulty lies in making the ability worthwhile and not a mild annoyance. That, I feel, is the problem with percentage-based speed reductions, such as what happens with medium and heavy loads; it remains a flat reduction, which can't increase nor decrease. It has its effectiveness, of course: it allows for a much more significant reduction on speed which penalizes the high-speed character, while leaving low-speed characters merely annoyed at moving slightly slower. And as well, it also allows for adjusting the penalty to changes in speed: Haste, for example, becomes needed but still less useful when the new speed acquired is reduced. However, the problem lies in being specifically fixed, much like all other speed reductions; it is a fixed reduction on a mathematically mutable ability, which is meant to worsen as time progresses.
I might cave into the proposal, but I feel that a mere 1/3rd speed reduction is not enough. Since it's really difficult to determine a speed reduction by means of percentage, this makes it hard to link the percentage progression through level (as in, 5-10% at level 3 and so on), but I might just apply the 1/3 flat speed reduction as if a heavy load, and apply the check penalty as if wearing heavy armor with Armor Proficiency (heavy), as per your second (modified) proposal. I'd love to go with 33% + 5 ft/2 levels progression, though; I feel it's the closest thing to a compromise, since eventually you'll find ways to force a speed lockdown. I might also limit speed reduction to 5 feet, since by the moment you're forced to move only five feet as a move action, that pretty much seals everything in stone (it's almost as bad as a lockdown).
Goodness gracious, no! Bez-Kismet is strictly an arcane class. Although, this may bode badly with other class ideas I might have...Looks fine. Dispel at 1st is very flavorful for this class (although if you every make a divine version you have archivist problems).
Hmm...I know I had a good reason why Balance, Climb and Jump were dropped as class skills, but for the love of goodness I can't remember. Just adding those three should make the amount of class skills reasonable enough for a 4+Int skill point selection. I was also suggested to add Sleight of Hand (odd, I know, but it lends to the vibe of the guy that fights smart and dirty) and Gather Information (even odder, since I find someone unsettling as the weirdest person to go look for information).If nothing else, please have 4 + int skills. If you do add skills, balance + climb + jump would be good choices. No reason to not have them. Perform could work.
I'll ponder on the Lethargy revision and the alteration to skill points and skills. I should also make a bit of space in the first post: I swear that when I made the edit where I cut Doom in three auras, the amount of info I added went well over the 50,000 limit (I think it's 50,000 word limit), and I had to cut quite a bit to make it short enough to post. And as you can see, it's insanely huge (although spoilered for your convenience)