Seeds for cacti are very small and store very little nutrition, once they germinate they are hungry but don't like strong fertilizer solutions because they are sensitive when they are young. A popular work about raising these cacti does claim that they do not need much fertilizer when they are young, but that has not be my experience.
I like a 20:20:20 type fertilizer and use it at one quarter to one half strength, fairly often like once a week.
I have seen the reddish pigment under pretty low light levels.
I seldom grow peruvianus types, I don't find them to be very desirable and they tend to be weak, they often grow slow. A few clones out there of them do grow about three feet a year in the right conditions, when well fed and given lots of light and not too much heat, RS0004 and SS01 are good examples of that.
hybrids, which I prefer, tend to the fastest growing in my experience, in a batch of seedlings it is not uncommon to find a specimen or two that is more vigorous than the others, it is these type of vigorous seedling that I have seen grow to about a foot tall in a year from seed. But I have also noted that many factors limit growth, food, light, roots space, pH of medium, heat etc.
One year ago I had seedlings that were about an inch tall, they were a couple of months old, now they are about ten inches tall, though one was a foot tall till I cut it yesterday because it was growing prostrate and I didn't want that.