So, the bases of the cacti shrink and turn green-yellow-ish and the yellow liquid is clearly visible. It has been like that for the past 4-5 months and I thought it would have recovered by now. Is there anything I can do to save it or should I just cut and clean it and start over?
Remove the small cacti and pot them in small containers (I mean adequated to their size). From the affected big ones I don't know if you can salvage anything, but you can try an experiment: cut the yellowish side with a knife, let the green part in contact with the air for a few days until the exposed tissue hardens, and then place it on wet sand. New roots may form.
If you let it the way it is now, it won't heal.
Update: I friend of mine that has a collection of cacti says that it is Mammillaria spinosissima v. albispina and the liquid drops are caused by an infection - she doesn't know what, so I can't say how or if the plants can be treated.