This exact question was answered just this Friday in the most recent FAQ posting on paizo's site.
Wild armor and other transforming armor: When I use a wild armor and gain the armor’s benefits, what restrictions, if any, apply to me? In general, when I transform with a polymorph effect and some of my gear melds into the form, what restrictions do I have for melding with large amounts of heavy gear? What about other types of transforming armor?
If you were in medium or heavy load from encumbrance before transforming, you continue to take those penalties in your melded form. Otherwise, ignore the weight of melded items and calculate your encumbrance in your polymorphed form entirely based on non-melded items. When wearing melded armor and shields, if you gain no benefit from the melded armor, you still count as wearing an armor of that type, but you do not suffer its armor check penalty, movement speed reduction, or arcane spell failure chance. If you do gain any benefits (as with the wild property), then you do suffer the armor check penalty, movement speed reduction, and arcane spell failure chance. This also applies to all other situations where you or an armor transform: you always count as wearing an armor of that type, and if you gain any benefit at all from the armor (such as mistmail), you apply the armor check penalty, movement speed reduction, and arcane spell failure chance.
It can be found HERE
Absolutely Not
As others have stated, no you can not use a focus (of any kind) while Wild Shaped, even if the animal you morph into has hands, and they are empty and holding the focus. All of the information you posted in the original question provides the answers for you so long as you cross reference them. But a lot of people have missed a crucial part of why it can't be done.
The description of the Druidic Focus says (5e PHB, p. 151):
A druidic focus might be [...] a totem object incorporating feathers,
fur, bones, and teeth from sacred animals. A druid can use such an
object as a spellcasting focus.
This essentially states that you get to create a focus out of whatever you deem worthy to call a focus; pretty neat.
The description of Material (M) components says:
Casting some spells requires particular objects, specified in
parentheses in the component entry. A character can use [...] a
spellcasting focus in place of the components specified for a
spell [but not costly or consumed components]
This is the start of the unravel. Here it says you can use a focus instead of a material component (so long as it has no cost/isn't consumed). So essentially focuses are just fluff/filler for material components that most people over look anyway, but if you don't overlook that stuff it's still a pretty minimal net gain.
Part of the description of the druid's Wild Shape feature says (5e PHB, p. 67):
- You choose whether your equipment falls to the ground in your
space, merges into your new form, or is worn by it. [...]
This portion infers that you get to wear or hold your focus if you so choose when you Wild Shape, which is pretty cool.
The druid's Beast Spells feature says (5e PHB, p. 67):
Beginning at 18th level, you can cast many of your druid spells in any
shape you assume using Wild Shape. You can perform the somatic and
verbal components of a druid spell while in a beast shape, but you
aren't able to provide material components.
This is the crucial spot. It specifically says no material components. If you recall from what exactly a focus is, it is essentially a fancy material component. Meaning it can't be used, not because you can't "hold" it, but because for Game Design purposes they disallowed it.
This is further backed up by the fact that they allow somatic components (hand and body gestures) even if you don't have hands or the appropriate body part to do the somatic component, i.e. a snake making a hand sign. So holding/wearing the material component/focus is irrelevant because it is completely outlawed in RAW.
The druid's Archdruid capstone feature says (emphasis mine):
At 20th level, you can use your Wild Shape an unlimited number of
times.
Additionally, you can ignore the verbal and somatic components of your
druid spells, as well as any material components that lack a cost
and aren't consumed by a spell. You gain this benefit in both your
natural shape and your beast shape from Wild Shape.
Doesn't this seem a bit redundant? It is because it is trying to show you that it is essentially an improvement to Beast Spells. At this point, once you reach 20th level you no longer need the material/focus component. So even at level 20 the answer is still technically no, but it becomes irrelevant because materials/focuses are no longer even needed.
However, this is D&D - so if the DM says, "Well that's stupid, you should be able to use your focus as long as you are wearing/holding it"... Then boom, there you go: the true answer is "yes, you can, so long as your DM handwaves it".
Best Answer
In the examples, Tygal's correctly using the feat Shaping Focus, but Nazghymbatulu isn't because the saurian shaman druid archetype delays Naz's wild shape ability until he's at least a Drd6.
A druid with the special ability wild shape who takes the feat Shaping Focus increases his effective druid level by up to 4 for the special ability wild shape but not beyond the creature's total character level
Thus a typical Drd4/Ftr3 who takes the feat Shaping Focus employs the special ability wild shape a if the Drd4/Ftr3 were a Drd7. (I chose the Drd4/Ftr3 instead of Drd4/Ftr4 because in typical campaigns the latter character wouldn't have a feat available at that precise total character level.)
However, the feat Shaping Focus can't benefit the saurian shaman Drd4/Ftr3 who, because of his archetype, until he reaches level 6 as a druid, lacks the special ability wild shape:
Prior to 6th level, then, a saurian shaman doesn't have the special ability wild shape. Therefore a saurian shaman Drd4/Ftr3 is unable to meet the prerequisites of the feat Shaping Focus and can't get the feat's benefits were he able to somehow.
Likewise a creature with no druid levels that somehow managed to take the feat doesn't gain the special ability wild shape as if the creature were a level 4 druid.
By analogy, the feat is like a coupon for extra 4 toppings on a pizza; one must still buy a pizza to get the extra toppings.