Let's start with question 2, because it's easier on me as the answerer.
Over in the mathematics and economics world, we like markets. I'd envision market system for Q&A.
Each student receives n units of currency (let's call them something sexy like MATH_Bux!) into a trust. They can only spend MATH_Bux! on answers. At the end of the quarter, student's MATH_Bux! earned for answers (those in the trust are not counted) are logged as a distribution and you scale 5% of their grade based on the MATH_Bux! distribution. 5% sounds reasonable to me as a student. This also sounds a lot like an answer to question 4.
On some sort of forum or something (I would use the internet for this), students may post questions from class (or independent study?) and answers. Students bid on which answer they like the best with their MATH_Bux!. I'd allocate myself, as the instructor, some fixed daily allotment of MATH_Bux! that I always spend within one week of accrual, to guarantee a certain level of activity (maybe do this with the students too, but then that punishes the student with an absurdly good idea in week 9 that is hailed as a genius by her classmates). I'd also post both questions and answers as a teacher, but never reward my MATH_Bux! to answers of questions I ask (to avoid bias problems). Hmmmm, this sounds like a good use of a sub-reddit. And it also sounds a lot like an answer to question 3.
To answer question 1, well, everything is better for graduates. They have more background and more dedication, so they'll take better advantage of something like this. But one of the reasons they're better at things like this is because they should've already done them as undergrads so I would be pretty optimistic for your undergrads. After all, if you've identified this as an important educational area, until a better way to teach it comes up this is all there is. I'd expect problems with participation (which is why I suggested a slight grade incentive), point trading (which actually still incentivizes some discussion), and concerns over quality (what I've experienced in Q&A classes, for which I generally recommend large numbers of examples).
And invariably someone will think MATH_Bux! is a silly name, and want dataPointz or something that isn't nearly as cool. Don't cave on that, MATH_Bux! is an awesome name and I'm sure everyone will learn to love it.