Not without a custom rom. The status bar is baked into the firmware. There are some apps out there that claim to allow you to modify it, however none of them work well or at all.
Yeah only with a custom firmware. Also it is only disabled on the lock screen if you use the clock lock screen widget. For example if you use the messages lock screen widget the clock shows.
no your right. The clock only disappears if you have the clock widget for your lock screen. I think the OP meant get rid of it all the time. Don't be to hard on yourself