It's the body_detail_plans that typically add the tissues to bodyparts, and they typically do so using the CATEGORY tags on the bodyparts. That's why leaving the [CATEGORY:HEAD] tag off the zombie head caused it to not have any tissue thickness.
The zombie head not having any thickness is also why it can't be damaged. Attacks will "pass right through" bodyparts with 0 tissue thickness. This is a potentially useful bug/feature,
although if you use it you will have to put up with the errorlog messages (see edit 3).
Also, you may want to do a custom body_detail_plan for the snake's skull head, as right now it's getting a layer of scales and muscle in addition to bone. EDIT: I note you HAVE a BODY_DETAIL_PLAN:SNAKE_UNDERHELL. You forgot to post it
You should remove the [CATEGORY:HEAD] tag from the snake skull and replace it with a [CATEGORY:] tag such that a layer of underhell bone gets added by your detail plan. Also, you can have underhell bone have no [VASCULAR] tag, so that it won't bleed if struck in the skull.
EDIT 2:
[TISSUE_LAYER:BY_TOKEN:SK:BONE] I suspect these should be BONE_UNDERHELL instead of just BONE
[TISSUE_LAYER:BY_TOKEN:JW:BONE]
[TISSUE_LAYER:BY_TOKEN:RES:BONE] ditto
[TISSUE_LAYER:BY_TOKEN:LES:BONE]
[TISSUE_LAYER:BY_TOKEN:REYE:EYE] This should have already been done by the default body_plan, since
[TISSUE_LAYER:BY_TOKEN:LEYE:EYE] The zombie eyes have the [CATEGORY:EYE] tag. Leaving them off doesn't cause an error message.
Removing the [CATEGORY:HEAD] tag from the skull and changing BONE to BONE_UNDERHELL above is enough to make the skull be composed on only underhell bone, and doesn't cause an error message.
EDIT 3: bleeding out is the bane of all creatures in Dwarf Fortress. Dragons too quickly die from blood loss if surrounded by even a small number of armed creatures. So in that sense your snake's problem is typical. In order to really last against multiple armed opponents, a creature needs to either be made of a hard substance and/or be unable to bleed, like the bronze colossus, or have a large number of distractor targets, like my balor and several of my illithid castes. In your case you might want to give the snake really hard scales and then include a number of small, "loose scales" that are easier to damage.
Also, I'm getting messages about attacks passing through the slime strands, which appears to be because your SLIME tissue says it uses the creature's SLIME material, but you never create a SLIME material and SLIME is not one of the materials created by the STANDARD_MATERIALS body_detail_plan. But this doesn't result in an errorlog error. Which is cool. But I suspect this is not what you had in mind.
Finally, this idea sounds pretty familiar. I have a feeling I should be saying hi to you.