Yes, the problem you are experiencing is a subclass of general flare and ghosting issues, often called "red dot flare" (see also: What causes lens flare?).

The reason for the grid or array appearance is because some of the bright incoming light is reflected off the actual microlens lens array ("individual" tiny lens for each sensor pixel) back towards the lens, then reflecting off of one of the lens elements back towards the sensor.

This particular form of flare/ghosting is particular to digital photography; it is precisely the physical characteristics of the imaging sensors (an arrangement of discrete photosites, arranged in rows and columns) that leads to this phenomenon. All digital cameras are subject to this issue. Some factors contribute to the degree of the problem, and whether it is noticeable:

• Smaller apertures (higher ƒ-number) make this issue more readily apparent, just like diffraction spikes that are more visible when a lens is stopped down. Basically, the red-dot flare is just small-aperture diffraction spikes convolved with a rectangular array.

• Higher ratios of sensor size : distance from rear lens element to sensor (notionally, registration distance) create more pronounced red-dot flare. Cameras designed to mount the lens comparatively close to the sensor bend the light more to cover the sensor. This bending (partially corrected by more aggressive microlens focusing) creates more dispersion of the light, resulting is more visibly discrete dot flares. Example: Fuji X-series review at photographylife.com.

Note that technically, this happens for every ray of light entering the camera, but you don't see it because of the degree of attenuation for each round trip. Note how dark the red spots are compared to the light source that causes the issue (sun, or other overpowering light in the scene).

In the third image you attached, I barely see any red dot flare (it's hardly red to my eyes, and it' so diffuse it could easily be confused with, or intermixed with, regular flare around the sun). The biggest anomaly is a single red ghost. Note how it is on the other side of the image, radially reflected opposite from the sun. This is standard, run-of-the-mill ghosting.