What is special about this type of capacitor? What are its characteristics? I can't find any info on them.
I expect it's a mica capacitor, often called "postage stamp" caps.
These have a thin rectangular molded case with colored dots.
Those are very reliable and stable. Failures have been seen, but that's a rare event.
I would never replace one unless it was proven to be bad, or physically damaged.
Note that mica caps have characteristics like temperature coefficient that may be critical to proper operation
of the circuit. Modern replacement parts may not duplicate those characteristics.
The value and other characteristics are normally denoted by colored dots.
There are many different "standard" formats, plus proprietary formats, using from three to nine dots.
Versions with more than six typically have dots both front and back.
A word of caution:
These can be damaged by moving them, particularly by rotating them around the leads to read the dots.
Note that other larger parts of the same general appearance exist, but they're long and skinny.
Such products made by Micamold are bad, period. They may be capacitors or resistors.