Even with no internet connection open 3G drains more power. In bad reception areas you may try yourself. My standard phone only cell phone dropped from 100% charged to dead within 10 hours with connected to 3G network (no internet connection logged in) instead of up to 7 days with 2G (its normal GSM and EDGE if logging in to provider network)
For what? If you do not look at it it doesn't matter if it is raining or not! Update at view is just enough.
Why refresh automatically? I have +50 new mails just overnight and another 50 in the morning hours... so I know there is new mail and it is up to me if I want to look, not up to my phone to annoy me with blinking or beeping or anything