I got my Captivate on Saturday. I haven't had the shutdown/reboot issue you are experiencing so there may be something up with that unit.
I agree with the initial battery consumption. I think I have my battery life issue sorted out. Basically it will involve shutting down stuff you are not using. For instance, right now, I am not using Bluetooth or GPS so I have those items shut off. If I am not going to be doing anything online for a bit, I turn off both wi-fi and mobile data (I can still make/receive calls though). I also use Advanced Task Killer to whack apps.
Here's a link to one set of tips regarding battery life:
linky