OK, there's a lot in that post...
I don't think it would be wise to put a sculpture into a portfolio for a painting program, but if it has painterly elements , as in, a sculpture that is hung from a wall-- that could be different and easier to talk about as an extension of your painting practice as well as being an example of how you're "pushing the boundaries of what can be considered painting." But, this could also just as likely be considered by the admissions officials to be pretentious and verbose wankery.
Dusseldorf's site doesn't have an English translation outside of the google translation. It's unfortunate, but I feel like I'm starting to understand it just from how much I've wistfully gazed at it...
About writing a Statement of Purpose, all schools have different desires for their "dream pupil" and varying strengths of their own... Some are more conceptually grounded, others focus more on practice. Hopefully most schools have a good balance of theory and practice, but that''s not necessarily the case everywhere. I didn't do this last year, but I'm considering tailoring my SOP to each school I'm applying to. THey're going to basically say the same things, but I think the emphasis on certain parts of my practice, artists that I look at, et cetera, have to shift around for different schools.
I can only remember 7 off the top of my head from last year's list. So bad...
CCA
Cal Arts
Yale
UT Austin
Hunter
Columbia
MICA
Also, It's important to apply to a LOT of schools if you actually want to get into one and get moving forward with this decision, and aren't stuck in some weird vortex of only applying to "the top" schools like I was last year. There are still about a billion people who want to be in an MFA program, no matter how much Dave Hickey talks smack about them.