Not sure when you attended Miami, but I think that Miami's ranking (to the extent that rankings mean anything) has been pretty stable since I graduated in 2003. From an undergraduate perspective, I'd say that OSU and Miami are equal academically (I was in a PhD program at OSU and taught undergrad classes). Both are good schools. Football and basketball have been pretty bad in recent years at Miami, so student apathy is understood.
True, but you wouldn't believe how many fans use it as the basis for their "My team is better than yours" argument.
Based on the transitive law of college sports, OSU should be ranked lower than Purdue (who beat Illinois). Then again, that means that Illinois should be ranked ahead of Indiana (based on games with Butler).