I can view the times I receive a new sms while my phone's on. Although, when I turn my phone off & turn it back on, it shows that I received my new sms the exact time I've turned my phone on but I want to see the actual time I've received it while it was off...
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I dont believe so no - a blackberry is designed as an always on device, hence why I dont believe RIM has made any improvement on the long start up time.

i don't think so

If the device is turned off, then you have not "received" the SMS until the device is turned on and has a signal. This is the time that will be displayed with the messages. If the time is important, do not turn the device off.