[sundberg]

I'm having a little bit of hard time understanding the somewhat unconventional (too me, anyway) carbonyl sterochemic nomenclature, re- / si-. Well, the nomenclature is not hard to understand but reactions with specific activity is hard to visualise.

If a re-specific attack on the carbonyl carbon would occur on the compound, what stereochemic outcome would arise? How should I think here? Does the attack come "straight into" the paper, so that the attached nucleophile will stick out of the plane and the hydrogen will go into it? (I really hope you  understood me there, because I almost didn't myself). Am I thinking correct?

[movies]

I think that you have the right idea since you have the Re and Si faces assigned properly.  The attack doesn't really happen perpendicular to the page, but rather at the Burgi-Dunitz angle which is calculated at about 109.5 degrees relative to the carbonyl C-O bond.  The products you have drawn look fine to me.

I find it easier to not redraw the structures to look at Re and Si.  Instead I will just draw it once and then identify which face I am looking at (that is, if the nucleophile where to attack from above the page) and from that I can tell the whichever side I am looking at, the other side (attack from behind the page) must be the other.

For reactions that select either the Re or Si face there is usually some kind of stereochemical model of the transition state where one of the faces is blocked.  Check out these papers for examples:

MacMillan, JACS 2000, 122, 4243-4244
MacMillan, JACS 2002, 124, 2458-2460