Assumption: All "skin" uses the same material attributes, and therefore all leather armor provides the same protection in combat, regardless of the creature it came from.
Question: is this true?
Mostly. Virtually all creatures use the standard skin and leather templates. However, some then alter these basic templates such that they have different properties. Usually (IIRC, in vanilla always) this only means altering temperature properties, but you could have a modded creature with abnormally-tough leather. Dragons are an example of a creature with altered properties in this case; they have a [SELECT_MATERIAL:ALL] line followed by a [HEATDAM_POINT:NONE] line, meaning that dragons and everything derived from dragons does not take damage no matter how hot they get. Dragon skin and leather would be just as heat-immune as the dragon itself, though this doesn't necessarily mean that it protects someone wearing it beyond simply not catching on fire.
Assumption: Bone is not the same across creature-types (the oft cited example of dragon bones being fireproof comes to mind). By extension, bone armor should vary in protectiveness by the type of bone, and the same goes for bolts.
Question: is this true?
In theory, yes, it's true, in practice it's false. Essentially, this is the same question as the one above, so the answer is the same: bones and shells get their properties from the basic bone and shell material templates, and could be modified in individual creatures but aren't beyond temperature effect alterations.
Assumption: cave spider silk cloth, giant cave spider silk cloth, phantom spider silk cloth, and forgotten beast silk cloth have the same attributes, and clothing made from them performs identically.
Assumption: pig tail cloth, rope reed fiber cloth perform the same
Assumption: ditto for wool cloth made from different animals.
Again, same thing. Could differ, but don't.
Lastly, is there any consensus on the most protective material type for clothing? silk cloth vs leather vs plant cloth vs wool cloth?
Silk is better than plant cloth is better than wool cloth by the numbers; the three materials have identical impact properties, but their cutting resistances go in that order from best to worst. Leather I'm not sure about; for the most part, its stats are identical or worse than wool's, but its elasticity values are better. A somewhat-educated guess suggests that since it bends less under a given stress but is pierced more easily than cloth it would perform better against blunt instruments but worse against blades. Actually, it's certain that it would perform better against blunt instruments than cloth, as all of its impact values are identical or better.
Basically, for blunt protection, leather is best and for edged protection silk is superior.