I did the annotation of that figure for the press release, so let me start by apologizing for the poor explanation, and then try to dig deeper into what's going on :) (although you already seem to pretty much get it right).
Lens models
The big orange galaxies all belong to a foreground cluster called WHL0137-08. For known point masses, there is an analytical solution to how exactly the mass deflects and magnifies light from background sources, but galaxies are not points, and we don't know their exact masses. Nevertheless, based on the observed distribution of light, assumed stellar mass-to-light ratios and stellar mass-dark matter halo mass relations, as well as assumed halo density profiles, we can estimate numerically how light from a background source travels through/around the cluster, and hence how it's magnified.
This is called a lens model, and because of these not always too well-constrained assumptions, there are quite a few different models. This is why the mass of Earendel is only constrained to within an order of magnitude, namely 50–500 $M_\odot$.
Caustic lines
A lens model thus returns a magnification factor for each 2D point in the vicinity of the cluster. In certain regions called "caustic lines", or just caustics, which lie along 1D lines, the magnification increases tremendously (in principle to infinity).
In the picture you see such a caustic, drawn in red. It bends smoothly around a handful of galaxies in the upper left corner, but where it comes close to the galaxy a little below the center, it bends around that one. The reason we're able to see Earendel is that it happens to lie almost exactly on top of the caustic.
Figure 2 from the paper (which isn't yet available online, but I think it's ok to share here with proper credits) showing the caustics predicted from four different lens models:
Credit: NASA, ESA, Brian Welch (JHU), Dan Coe (STScI).
The red curve that I used in the image you post is the "Light-Traces-Mass model" (LTM; Zitrin et al. 2015). To understand the effect of the uncertainties in the model, the posterior distribution was sampled and used to generate critical curves from each resultant parameter set. Those are the thin brown lines close to the red. In 80/100 of such model runs, Earendel is within 0.1 arcsec of the line, with a maximum of 0.4".
Mirror images
If an objects lies close to, but not on top of, a caustic, its light will be bent around it and reach us from two different directions. Close to Earendel lies a small star cluster (called "1.1" in the paper). Because of the way the caustic bends, 1.1 is mirrored not twice but three times, indicated in cyan. In fact there's a second star cluster called "1.7" that I didn't mark, to keep it simple, but you see it as slightly enhanced dots of light along the red arc.
Arcs
So, what is that red arc? That's the host galaxy — called WHL0137-zD1, but nicknamed the "Sunrise Arc" — of both the star clusters and Earendel. This is a typical feature of gravitational lenses, distorting background galaxies to banana-shaped arcs along directions which are more or less tangential to the cluster. In fact, the Sunrise Arc is one of the longest known, being 15 arcseconds long.
Magnification
The term "magnification", usually denoted $\mu$, is used both for the increase in area and the increase in brightness. Usually, if you zoom in on an image of some object, the brightness is conserved so the surface brightness decreases. But with lensing, surface brightness is conserved, so the total brightness increases.
Stars are much too small to be spatially resolved by our telescopes, however, so they are seen as point sources. In principle their sizes do increase when they're lensed, and in principle they may also be elongated, but they are so small that they're still way below our resolution, and will always be seen as point sources. Hence, for stars the magnification just refers to the increase in brightness.
If Earendel is 10× the diameter of our Sun, its angular extent seen by us would be $\sim10^{-10}\,\mathrm{arcsec}$. Even if Earendel is magnified $10^5$ times — the estimated maximum according to the lens models — it's still of the order of ten microarcsec, unresolvable by both Hubble and James Webb. This resolution is actually within reach for interferometry, but that would require Earendel to be bright in the much longer wavelengths required for that technique, which it isn't.
