iMac and external with time machine q's

I bought an external HD (1TB) and hooked it up to my computer. The icon sits on the bottom left side of my desktop *orange*. The time machine backs it up when its suppose to but when I power down into sleep mode, a LOT of times it will flick back on immediately and tell me I forgot to eject the disk.
I click ok, then put it into sleep mode and its fine.

This happens A LOT!

THEN I will power it back up and do my work and sometimes when I power it back up it will freeze and many things *finder, most of the time* will freeze.
Then I will put back in sleep mode and it will freeze again.
I can usually just force quit whatever application has caused me a problem but the frequency increases on the number of times it tells me I forgot to eject my disk.
I thought the point of having external/time machine was to leave it plugged in all the time?

Two weeks ago I just unplugged it and figured I'd just plug it in manually once a week and back up. Since unplugging it, I haven't frozen at ALL.

So .. what am I doing wrong?

And when I do plug it in manually, where do I go to get it to instantly do a back up instead of waiting an hour?

Help

....
Ok, I've had it plugged in for twenty minutes now and I put to sleep and it popped back on already with the failed to eject message and then now within five minutes I've had entourage freeze and finder.

Its been unplugged now.