U have some kind of mold on your cacti. But pretty harmless. Your cacti is big enough to fight off the invaders.
Spiders/eggs theory is really interesting but haven't heard for any infestation more then 1/4 of my life(I'm 24).
Spiders love leafy plants, not cacti. Only couple endogenous-specie of slugs/snails can eat Echinopsis cacti. But U doesn't live in Peru and your cacti isn't from Peru, and after all U doesn't have slugs! LOL
What also this could be? Where U keep your cacti?
Maybe cold shock, heat shock, dry/moist air shock, low watering or mineral deficiency is problem with such symptoms.
Cacti, bigger cacti knows to act weird, every grower knows that cause we have experienced it.OK, maybe someone panic and call it disease which it isn't(dangerous disease). Some examples:
Small cracks on skin turns into greener skin dots or in other hand turns into "wood". Hard like wood and look like piece of wood shoot down into cacti. Like common wood, just look at your parquet and U will see thousands dots, stripes, discolorations and colorations, hard/soft degree variations, and other stuff.
Where U keep your cacti? Near which plants? Do U know that plants are like people? I heard that more then 100000 times from family, wise surrounding people and cacti growth mentor!, I am betting that U have also heard that from someone.
So have U heard for allergies? Yes, some plants can literally suffocate and diminish other plants like THAT! Similar sibilance bout grass under tree/forest or weed in vegetables.
Do not use chemicals and don't even try think to cut down this beautifully cacti!! Cutting is last resource! BUT REALLY!!
My special treatment tip for U is this. First cut of little piece of that "infestation, spiders, molds, autoimmune, cancer" symptoms(0,25X0.25mm). Place it under strong light and observe it like cyclop doctor!
Observe and write down (post here) what is happening. Is it soft, hard, moving?, dry, moist and so on and decide is that spider or something else but if U are in dilemma afterwards, leave it under glass/cup on white paper. If U can maybe spare one more cut-dot also use colored paper. Black is the best. Why? Color (RGB, white and black) on white/black background can easily show two different colors.
After that if U want to know everything what is happening, place those cuts under strong lamp or on radiator. Try to dry it in 24 hours. But don't rush the process. Leave it be, naturally.
Post me what U see. After such observation I will know whats really wrong, in Latin! But unexperienced grower will also find out what the hell is going on. Exchange of info here on this forum is supreme guidance!
HOME MADE MEDICINE:
Smoke one cig.
Took ash and mix it with water. One cig on 1-2 spoons.
This mass-herbal mixture cure must cover infected or/ cutting or/ damaged or/ rotten /soo on, area on cacti. Mix ash with water and then take sponge or something like that cause U need to "spray" whole sick area and 15% more around. Leave that for one day. Mixture will fall of by itself. Do that if U think that U need it.
3days and after cacti shape will become better. Hopefully problem will "fall off" also.
One mention: this mix isn't dangerous in any kind. U can even put it into eyes.LOL
Hope that am helping U?.
Peace
Light
Love
Bless