While very subject to interpretation, here is my 2 cents:
Knight of the weave: Your caster level for your knight spells is equal to your knight class levels plus any other arcane "Caster Levels" you may have
Master Spellthief: Your spellthief and arcane spellcaster levels stack when determining your caster level for "all arcane spells"
I would not add your spell thief levels to the wizard ... I think you calculate the wizard first, then add to spellthief, and then use that for all.
Wizard = 15 levels + 3 UM + 3 tattoo + 1 ring = 22
KotW: 5 levels + 22 wizard (I wouldn't count the following twice: + 3 UM + 3 tattoo + 1 ring) +5 master spellthief (to be sane ... raw, it would be an infinite loop) = 32
Spellthief = 5 + 4 + (I wouldn't count the following: 3 + 3 + 1 ) + 22 + 32 = 63 ... and you use this for "all arcane spells"
Do I add both Wiz and KotW CLs to the Spellthief CL?
. I'd say yes. "arcane spellcaster levels" Note, that one could argue this was supposed to be only class levels, but I think caster levels makes more sense.
What's the final CL for transmutation and illusion spells (each of which gets boosted +1, from Robe and Illusion Mastery), taking into account Theurgic Specialist?
First I'd take the +1s into account, then:
I'd triple your CL ... (Wiz CL) + (KotW CL) + (spellthief CL) = Spelltheif CL * 3
Do I add +6 for Silent Image (or more) from propagating Arcane Thesis across all 3 classes, or is it only +2 from applying it on top of everything else?
Frankly, it's broken enough, so I wouldn't. But once again, this is a mix of RAW and David's interpretation of the semblance of sanity.
Best,
David