1) Can't be done without eliminating BIS/BES, and then using a 3rd party app for mail.
2) Could be the OS, but I'd contact the carrier. It might be due to improper advanced settings they can talk you through, or a faulty antenna.
3) Issue #2 is probably the biggest impact on your battery. Close apps not in use, don't have push apps refresh frequently, cut down the screen intensity, cut back the time the screen stays lit.