1. buy T&FN's Big Green Book. The answer to this and all your other conversion questions can be found there.
2. 3:13.57 (4x400m) is a superior mark to 3:16.5 (4x440y/4x~402.5m).
3. If 3:16.5 for the MILE (4x440y/4x~402.5m) relay, not 4x400, then it is the "state record" for the MILE relay.
4. Ohio doesn't appear to recognize the MILE relay as an event. It recognizes the 1600 meter relay so there really is no Ohio MILE relay record.
5. If you're don't care or can't figure out what distinctions are being made here then refer to #2.