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How can I tell if it's doing something?
Start up Activity Monitor (In the Utilities folder) and click the "Disk" tab.
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could someone remind me how to get into this to change the automatic backing up schedule (step by step, please, and pictures help if possible)
I assume you are talking about the SuperDuper schedule? Even without pictures, it's pretty simple. Did you look at the Window menu? In there is a "Scheduled Copies" item. Select that and there's your schedule. If you want to change the current schedule, I think the "Edit" button might be a good place to start. 
If you're talking about Time Machine, it's schedule is once every 60 minutes. It can be changed but I don't recommend doing that. Just let it do its thing. After the first backup, the rest will be extremely fast. That first one could have been why your external drive was so busy for so long, especially if you were doing a SuperDuper backup at the same time.
When you get a chance, how about updating your TS Profile so that most of your new hardware will be visible when you post a question. That makes it often much faster to get answers since you won't have to answer questions about what hardware/OS version you're running.
Near the top of this page, just under the banner image is a "My Controls" link. On the page that takes you to, look along the left-hand side for a "Edit Personal Profile" link. Then, on that page, near the bottom is a text box labeled "My Macs" that will store the hardware/software info. Thanks for doing that!!
When you changed computers you removed the drive that SuperDuper thinks it is supposed to backup to the external. Even though your computer's internal drive is named "Macintosh HD" there is other information about it's identity. SD knows it's not the same "Macintosh HD" anymore, it's still looking for the old machine. "Macintosh HD" (BYW, I think there is a space between "Macintosh" and "HD") is simply the default name for the hard drive in all Macs.
The easiest way to tell it what you want is to simply delete the old schedule and create a new one.
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You've selected External Hard Drive to as the location to copy to. Now select the location to copy from in the first pop up.
A "pop up" is simply a list of items (hard drives, in this case). They are usually indicated by a 'double-arrow' icon on the right-hand side of a button. In this case, the 'pop up' button is the one next to the "Copy" label. Click it and you should see every hard drive that SD knows about. Just select the one that says "Macintosh HD". Notice that there are three more buttons on that little window. The three at the top are the one you use to select the drive to be copied and where it will be backed up. The other, longer button tells SD what kind of backup to make.
So, select your 'new' "Macintosh HD", leave the 'to' selection as you had (whatever the name of the external drive is), and then select the "Options" button. Now, you have two more pop up buttons. The first one tells SD exactly which type of back up method to use, most of us recommend the "Smart Update [the name of the external drive] from [the name of the internal drive (Macintosh HD, in this case)]" method. The other button just tells SD what to do when its finished, I have mine set to just Quit.
Now click "OK". You can now make the backup or click the "Schedule" button to edit the current schedule. You may see two schedules, if you have not deleted that previous one. Hope that helps.