You pick whatever time you want. There's no "available" time slot like with Yahoo. Just choose whatever date/time works best for your guys.
That was my assumption. They call out their draft pick, you sit there with the draft applet and make their picks for them. The commissioner on Sportsline (unlike Yahoo) has the ability to pause the draft, back out accidental picks, and make picks for other teams.
The offsite guys will see you picking players in real time. It's no different to them than if all of the players were remote and doing an online draft.
You can set it up, and look at the draft applet. Hell, you can even make picks, do whatever you want, and then just reset the thing and start over (I think you may need to send Sportsline an email to get them to clear it out and re-set everything.