Yes, you can capture directly to the external drive.
And do you leave your Mac on overnight?
"OS X does its own cleanup operations every now and then, getting rid of old temporary files and other junk. Unfortunately, these cleanup routines are scheduled in the middle of the night, so it won't run if your Mac isn't turned on then. " (Fixed in Tiger)
Also, check out
this program...it'll tell you exactly how much space each folder is taking up and such...you can go through your whole computer quickly and see what's taking up what.