1. Is this really a program that is set primarily to gain mass? (since it's the "Animal Mass" version)
yes, it is, although no program helps you gain mass unless the diet is there too. for mass, though, it's got the key ingredients - major compound lifts in low volume, and enough recovery time built in for most intermediates, i think.
2. What is meant by "low volume" (behind accessory)? How many exercises/reps/sets, and apparently you can choose which exercises. What's the deal here? (What's best?)
"low volume" means that you're doing low everything except weight: not very many exercises, not very many reps (3-8 usually considered 'low volume'), and not very many sets (3-5). you still use heavy weight, though. i'd probably just do some kind of tricep extension (skullcrushers maybe) for 3 sets of 5 myself, and then weighted situps for the abs.
3. According to this program you train your abs 3 times a week. Suppose I would train my abs on the other 4 (non training-)days at home too, will this get me to that rock hard six-pack faster or is that over-training?
two things here.
1 - six-packs have much, much less to do with lifting - if anything at all - and more to do with cardio and diet. you need to strip away the fat covering your abs for them to actually show through; doing 400 situps, or doing a bunch of weighted situps isn't going to do much for display purposes. doing heavy ab work is about building core stability, which helps you in all of your major lifts and in any athletic event you do.
EDIT - i forgot to mention one thing, which is that twice i've mentioned diet, and i meant them differently, the diet you'd use to gain mass is not the diet you'd use to lose fat, you can do both at once but it's very difficult. if mass is your primary gain i wouldn't be so worried about a six-pack for a while, more muscle will speed up your metabolic rate anyway.
2 - there is certainly a point of overtraining. to quote Mark Rippetoe:
"If the stress on the body is too great, either in magnitude or frequency, the body will be unable to adequately adapt and exhaustion will occur [...], which we typically call 'overtraining'." (Practical Programming for Strength Training, p. 26).
so, yes, there is definitely a point of doing too much and working the same muscle 7 days a week is way beyond that point. just do abs the days that the program says to do abs and you'll be fine.