He explains that the Higgs boson is a particular excitation mode of the Higgs field, but what is then the (general) 'ziggs' boson? Are Higgs and ziggs actually the same?
If there was only a massive $Z$ boson, and nothing else, then this 'ziggs' mechanism would be sufficient and the slightly more complicated 'Higgs' mechanism would not be required. I would look at the 'ziggs' as what the 'Higgs' would look like in this scenario.
The Z boson has been known experimentally for decades, what about its weakly hypercharged product? Does the Higgs boson actually have nothing to do with the Higgs phenomenon, being merely a consequence of the theory that was begging to be discovered experimentally?
I presume by 'hypercharged product' you mean the charged $W^+$ and $W^-$ bosons. These are not products of the $Z$ boson, instead they are all a part of the same family of particles. Well its actually a bit more complicated than that... let's start from the top. The Higgs mechanism 'starts' with four massless bosons ($B^0$,$W^0$,$W^1$,$W^2$), which after some interacting with the Higgs field, will produce three massive bosons ($Z$,$W^+$,$W^-$) and one massless boson (which is the photon, $\gamma$).
As there are four original bosons, without going into the heavier details, this means that the Higgs-field should be constructed from four components (or degrees of freedom). After interaction with the four components of the field, the four original bosons acquire a mass. However - as mentioned earlier - the photon is massless. In order to add this condition into our theory, we mix two of the original four bosons (the $B^0$ and $W^0$, which have no electric charge) to produce the the observed $Z$ and $\gamma$ bosons in such an exact way as to leave the photon massless. The repercussion of this is that we are left with one free component of our Higgs-field, remaining from our original four-component Higgs-field. This spare component, analogously to the 'ziggs' mechanism, manifests itself as the Higgs boson.
Yes, an electron is just some wave, as you say, in the electron field, as it is for any particle. You can also interpret in a broad sense that a field needs to be perturbed at a particular point in spacetime for you to have a non-zero odd of measuring it a that point, although this simple picture is complicated by quantum phenomenas.
The energy of a decaying particle not only can but needs to end up somewhere. This is conservation of energy! The mechanism are not unknown, they are the possible interactions (read that as forces) between fields, though they are not all clearly understood in their dynamics.
The idea of billard balls particles colliding is really not the best to have in mind when considering QFT. The electron, which is really a wave/excitation in a field, travelling in spacetime in presence of the Higgs field does not need to ''collide'', in a classical view, with a Higgs particle to interact. Keep in mind that these field excitations are not exactly localized, much as a wave is not. What happens is that the electron field interacts with the Higgs field and as seen form the dynamic of the electron field it corresponds to it having a mass. The closest analogy that comes to mind, which is pretty bad: don't give it too much intellectual weight, is of a bullet going through water that acquires a different dynamic behavior by interacting with the surrounding media, but that's as far as it goes.
Your question about the difference between a Higgs particle and another one, is like asking what is the difference between sound and light. They are not excitations of the same medium.
I am sadly not aware of any good and simple analogies for the Higgs mechanism. The closest thing, which is not simple but quite close conceptually speaking, are electrons in crystal having a different effective mass because of their interaction with the crystal lattice. Without using effective field theories, you can model electron wavefunctions moving in the crystal lattice using standard quantum mechanics. From there, you study their dispersion relation which is in essence the equation relating energy and momentum. The dispersion relation, in some cases, will take the a functional form of a free wave from which you can infer an effective mass. You can interpret that as saying that the interaction with the lattice modifies the mass of the free electron.
Best Answer
The mass of a fundamental particle turns out to be quite an elusive concept, because massless particles act as a source of gravity and they carry momentum. What then is special about mass?
Where mass comes in is in explaining the relationship between the total energy of a particle and its momentum. For any particle we have the expression for the total energy:
$$ E^2 = p^2 c^2 + m^2 c^4 \tag{1} $$
where $m$ is a parameter that we call the rest mass. It's the parameter $m$ that the Higgs mechanism gives us.
I can't see any way that either of the options you mention could usefully describe the value of the parameter $m$ in equation (1). For example, why would the electron, muon and tau have such different rest masses when they are all (as far as we know) point particles with the same charge?