I don't think my old Palm Centro, from which I just migrated (more on that later) even has a "totally off" setting--other than removing the battery. I cannot recall ever "switching off," totally, any wireless phone I've ever had, since my first one: A Motorola Contour on Ameritech.
Now ponder what you wrote, there, for a second. If it "switches itself on," how could it ever have been truly "off?"
Here's a little not-so-secret-secret: Most modern appliances (i.e.: TVs, other entertainment devices, appliances, etc.) never actually "turn off" when you turn them "off." They just... nap. How else could your TV, for example, be turned on by the press of a button on a remote?
As I noted above: I'm just migrating from a Palm Centro to an Android "smart"phone. There are certainly things I miss about my old Palm device, but I'm finding my Android device appears to be more than making up for those things by supplying additional new functionality.
As for the text message time & date thing (looks...): The text message app on my HTC Sensation 4G gives me date and time on each. As for alerts: It blinks the led indicator, that's also the charge indicator, for any notification. I wish it would occasionally make an abbreviated notification sound, until the alert was acknowledged, like my Centro does, but, like I said...
Here's the test: Use your new handset for, oh, say a month. Embrace it. Learn it. Truly use its capabilities. I don't mean make stuff up, but use the things that make sense for you to use. Then pick up your old phone and see if you think you could go back to it. (Some people can and do, btw.)
Jim