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 exact mechanism of producing neutrino mass is not known. The main problem is that the neutrino masses are extremely tiny compared to all other energy scales. That means that any interaction responsible for their appearances is highly suppressed.
The massless fermions can be described by the so called chiral spinors, left or right. That correspond to the left/right helicity (the projection of the spin on the particle momentum) of the particles and the opposite helicity of the antiparticles. It's interesting that the weak interaction involves only the left spinors. When we assumed that neutrinos are massless we used only one left chiral spinor $\nu_L$ to describe each sort.
However for massive fermion you can always find a reference frame where it moves in the different direction. Therefore the helicity of the massive fermion is not invariant. This is connected with the fact that to describe the massive fermion you need to get some spinor of the opposite chirality. The most straightforward way (known as the Dirac mass) that is realized for charged leptons and quarks is to mix two different spinors with opposite chiralities. If we assume that neutrino masses are realized by the same mechanism we should introduce extra spinor $\nu_R$ and couple it to $\nu_L$ using the Higgs field with some vacuum expectation value $\langle v\rangle$. Then at the low energies we would obtain in the Lagrangian, \begin{equation} g\langle v\rangle \nu_R^\dagger\nu_L+g\nu_R^\dagger h \nu_L+\mathrm{h.c.} \end{equation} The first term correspond to the mass of the neutrino equal to $g\langle v\rangle$ and the second describes its interaction with the Higgs particle $h$ which is represented by the following Feynman diagram vertex.
The issue is that the neutrinos are very light compared to other fermions. That means that the coupling constant $g$ for neutrinos should be extremely tiny compared to e.g. the one for the electron which seems rather strange. As $g$ determines the coupling constant for neutrino interaction with the Higgs particle that means that such processes are extremely suppressed. As the neutrinos are electrically neutral and $W^\pm$, $Z^0$ bosons interact only with $\nu_L$ the new component $\nu_R$ doesn't play any role in any other proccess. So we have to introduce practically invisible new field using some strange values of parameters.
The other way (so-called Majorana mass) uses the fact that particles and antiparticles coming from the same chiral spinor $\chi$ has opposite chiralities. So the charge conjugation $\chi^c$ of that spinor behaves as the spinor of the opposite chirality and we can use $\nu_L^c$ instead of $\nu_R$. Because of the weak interaction to make a theory self-consistent you have to couple them also to the Higgs field in the following way, \begin{equation} \frac{g}{\Lambda} (\nu_L^c)^\dagger h^2 \nu_L \end{equation} This describes the different interaction with Higgs particle represented by the following Feynman diagramm vertex,
Now the coupling constant becomes dimensional characterized by some large energy scale $\Lambda$. That means that our model becomes non-renormalizable i.e. it will be broken when our energies becomes comparable with $\Lambda$. Therefore adding Majorana mass to neutrinos means that we touch some more fundamental new physics. This can however explain why those masses are so tiny - in this hypothesis they are actually a weak echo of some new physics at very high energy scale.
You can actually get this Majorana neutrino with a very simple so-called seesaw mechanism that combines usual Higgs mechanism involving new component $\nu_R$ with some very heavy Majorana mass $M_R$ for $\nu_R$ (that can be introduced in the renormalizable way as it doesn't interact with the $W^\pm$ and $Z^0$). It's interesting that if $M_R$ is comparable with the hypothesized Grand Unification scale whereas interaction with the Higgs field is almost as strong as for the electrons the resulting mass for the light neutrinos has order close to the observations. Because this mechanism is so simple and natural this is quite popular hypothesis.
Of course those are the simplest options. It may be that neutrinos don't interact with Higgs directly at all and its role is played by some unknown fields with similar properties but much higher mass. We simply don't know yet.