In the man's part of the 3-step (e.g., international foxtrot), the count is slow (left foot), quick (R), quick (L). The way I learned it, it's heel, heel-toe, toe-heel. Between the two quicks, is there (a)normal rise/fall (b)slight rise/fall or (c) no rise/fall?

First of all, in the "Ballroom Technique" of the ISTD (former: Alex Moore) the nrs of the steps are different, but I'll treat them as you counted, because for better clarity they are often taught that way (correct numbering would be: your 1st step is the last step of a preceeding figure, e.g. a feather finish / feather step, which is described with 4 steps, the Three Step then starts at your 2nd step, counted QQS, with the last step beeing identical to the first step of the next figure.)
But let's stay at your counting of SQQ. Generally we have to distinguish between a continuous rise as used in Slow Waltz to create maximum swing, that is denoted by "commence to rise e/o 1, continue to rise on 2 and 3 ..." - this is done e.g. at the basic turns in Waltz, "Natural Turn", "Reverse Turn". Then there are figures with a faster rise as e.g. Natural Turn in Quickstep. There we say "rise e/o 1, up on 2, up on 3 ..." which means, the rise is not that continuous as in Waltz, where you swing higher and higher, but you nearly reach full height (which is less than full height in Waltz) already on 2.
Now our Three Step: "rise e/o first Q" means doing it Quickstep like, with one difference: you are doing it FASTER because it's done from a Q and you stay up for a very little time, the 2nd Q which already has a lowering at its end. At last I would say, it's a "middle height" (remember: highest point of all ballroom figures is step 3 of Waltz's Nat./Reverse Turn.) And you have to take into consideration that the lady's rise is restricted by "No Foot Rise". "Middle rise" because there are figures with less rise, e.g. man's Wing, or 4-6 of the Rev. Turn in Viennese Waltz (and of cause there are figures with no rise, e.g. 4-6 of Hesitation Change ...)

German Dance Teacher. Very nicely explained. But can anybody tell me why the last step of the Feather is the first step of the Reverse Turn. The Feather Finish in the Reverse Turn is the same. As is the Third Step of the Three step. The Three Step starts on the mans right foot and is a quick. This must be very confusing to a person trying to learn from a book.

I) Why has the Feather Step (Feather Finish) been described with 4 steps in the Technique?
I think it's that way to point out the difficulty of the movement after step 3, which is:
a) ending in CBMP - so you have to get the lady back into normal position between 3 and 4
b) for the lady with front-foot-heel on the floor (resulting from NFR) - so she has to pull R heel over the floor between 3 and 4.
Many ballroom figures include the "next" step of the following figure at their end to indicate "how to go on.": e.g. last step of any Chassé, Outside Change/Weave (Waltz) ...
At these figures the last step is identical with the first step of the next one, but ... -> II

II) Why doesn't the Three Step start with LF (identical to the last step of the Feather Step)?
That's a hard question. I think, there are two (weak and speculating) possible explanations:
a) To point out the peculiarity and accentuation of that first Q. Perhaps it was wished to guarantee that this step doesn't drown between the others.
b) The last step ('S') (identical to first of next figure) has to be included in the desciption of the figure for similar reasons as in (I). And if so, the THREE Step would have 4 steps if the preceeding S would be included.

III) Problems by learning from the book.
By looking at the "Preceede" and "Follow" sections this problem of the lack of clarity can be reduced.
AND: Don't learn from the book ONLY. Use videos or even better a good dance instructor!

German Teacher. I tried to explain to a person trying to learn from a book that the Feather Step finishes on the left foot for the man which then becomes first of the Reverse Turn. Same thing on the Feather Finish plus the last step of Three Step which becomes the first of the Natural Turn. She said why ?. I said I haven't a clue. Has anyone ?.

Maybe it's because of the lowering. You can't lower the foot on 3 and keep the back foot in place.

I'm an educator by profession myself (though not in dancing, i hasten to add).
Text books are written by humans. When i recommend text books to my students, i'm acutely aware that they all have their faults (the books i mean!).
I think the problem is that the text books simply are not rigorous in their definitions. Having the last step of one figure being the first step of another figure is bound to cause confusion. Confusion slows and undermines the learning process.
By the way - German teacher - your posting was excellent