The simplest way is to have the cron job itself signal to you somehow, perhaps by creating a file when starting and removing it when done. What's tougher is if there needs to be some mechanism to figure out whether it's really only just working and taking time, or hanging. Perhaps your best bet is to make it verbose enough that you can tell when it's not working simply by observing the lack of output.

Your second question seems to be about redirection; yes, you can redirect standard output using 1> and standard error using 2> like this:

(The "1" is implicit in the first redirection, and often left out.)