If I hook a slingbox up to one of these dvices (which I assume IS required), can I watch TV over the internet, while also watching a different channel through that same device?
The only way to avoid interactions between the remote viewing of the Slingbox and local viewers of the television is to tap into a video source that isn't currently being viewed locally.
The Slingbox isn't a magical device it can only rebroadcast what it "sees" and "hears". There are a few devices which have multiple tuners and segmented autonomous outputs. This is normally meant to be used as a cable feed for a remote TV. If you have such a set-top box then it you can connect to the Slingbox to the secondary output without affecting local access. However, most devices have this type of output.
The Slingbox Pro-HD has a hybrid analog and digital tuner which allows you to watch television without affecting local viewers. The tuner is compatible with over the air ATSC and unecncrypted QAM signals, so you'll have to check with your cable company to see if they broadcast any channels which is compatible with the tuner.
So, the answer is, "Maybe".
What I mean is, just because I have a slingbox connected, do I control whatever is shown on the TV that the comcast box is connected to?
That depends on what you're hooked up to, and the configuration within your entertainment system.
I'm asking this because if my family is watching TV that the box is connected to, and they want to watch the news, and I want to watch the NFL game, would that be impossible?
Yes, depending on your equipment, which SLingbox you purchase, and how you intend on implementing it within your home entertainment ecosystem.
I'm under the impression that the slingbox changes the chanel of the digital box, so if someone turns on the TV at home, they will be on whatever chanel that I would be watching through the slingbox.
Yes, that the common configuration of set-top boxes which do not support multiple channels and segmented autonomous outputs.