Are there in nature any Right Chiral isolated electron particles? Note: I refrain from using the concept of handedness and the terms left-handed and right-handed when referring to chirality since these usually refer to the helicity of charged fermions and their antiparticles and prefer to use instead the terms referring to their Lorentz invariant but not a constant of motion chirality, namely as Left-Chiral and Right-Chiral similar as looking statically at your two hands without any momentum involved. These handedness above terms sometimes used in common for either referring to helicity or chirality I find a big source of confusion even for the related WP pages references.
My question is:
It is stated in WP Chiral Theories,

"Particle physicists have only observed or inferred left-handed
fermions and right-handed antifermions engaging in the charged weak
interaction."

In the above quote WP uses the terms left-handed and right-handed referring to the chirality of these particles... ):
Since a right-chiral fermion would not carry any weak hypercharge thus it does not interact with the Higgs  that would strongly imply that this electron does not gain any mass from the Higgs field. The same is also true for a left-chiral antifermion like a left-chiral positron (i.e. only right-chiral positrons carry a weak hypercharge).
But a massless electron cannot be described anymore as a physical electron.
Therefore I'm asking are there actually in nature any right-chiral isolated electrons or is this just a mathematical induced physics effective theory used in order to describe the Higgs mechanism?
 A: I would strongly disfavor your associating handedness with helicity instead of chirality, but no matter... Indeed, the WP usage of right-handed for right-chiral (annihilated by $1-\gamma_5$) is fine. It is a source of clarity, not confusion. In this issue, helicity stays out of the picture, regardless of language.

Since a right-chiral fermion would not carry any weak hypercharge thus it does not interact with the Higgs that would strongly imply that this electron does not gain any mass from the Higgs field....

Right-chiral fermion fields have a hypercharge proportional to their electric charge, by the (EWeak) Gell-Mann—Nishijima formula. They do interact with the Higgs field, in the Yukawa terms of vanishing total weak hypercharge. These terms couple right-chiral to left-chiral fermions and induce the fermion masses through the v.e.v. of the Higgs field, of course. (Charged current weak interactions refer to W couplings, and not Higgs couplings.)
Right-chiral electrons exist, and they are, on average, half the degrees of freedom my and your and the universe's electrons have.
They are never isolated, as the electron mass connects them to their left-chiral brothers.  Chirality is not constant in time. They have little to do with the Higgs mechanism. (I hope you don't actually mean SSB, instead).

 NB There is a pedagogical picture presenting this as a chirality oscillation controlled by the mass term in the hamiltonian. A stationary solution of the free Dirac equation dictates immediately, starting from the R state,
$$
\langle \gamma_5 \rangle =  \cos(2mt).
$$ 
A: Left-chiral and right-chiral electrons don't exist as isolated long-lived objects.
Instead, what we call an electron (with rest mass $m$), is
actually a particle constantly oscillating between
being a left-chiral electron ($e_L$) and a right-chiral electron ($e_R$).
The frequency of this oscillation is extremely high,
$\nu=\frac{mc^2}{h}=1.2\cdot 10^{20}\text{ Hz}$.
Every time the electron changes from $e_L$ to $e_R$ or vice versa,
it emits/absorbs a boson to/from the
ubiquitous Higgs field which permeates the whole world.

Here I have paraphrased what I understood from Leonard Susskind's lecture
"Demystifying the Higgs Boson" (especially in time 42:30 - 51:40).
A: In its rest frame, an electron is an equal superposition of its left-chiral and right-chiral components.  The two pieces transform differently under boosts, for reasons which occupy a chapter or two in textbooks on field theory.  So if you are holding a polarized electron in your hand at rest, you’ll think it’s equal parts left- and right-chiral.  But if I run past you relativistically, I’ll see your electron as one chirality or the other depending on whether I run at its “north pole” or its “south pole.”
The charged weak current only interacts with the left-chiral parts of the matter fields, and with the right-chiral parts of the antimatter fields.  In the rest frame of the decay, electrons created by the charged current are purely left-chiral, and so the more energetic they are, the more strongly they are also left-polarized.  But in the rest frame of the created electron, it is equal parts left- and right-chiral the whole time.
