1. You can sling from Utah to your Maine residance just fine.
2. You could watch something difefrent in your senatrio if you added another DirecTV receiver to your account that would be dedicated to the slingbox's use. If you plan on using your current DirecTV box that would not be the case as if one person was watching locally and changed channels it would change for the remote viewer in Maine.
3. although you have high speed internaet access at both locations, quality depends on your ISP's speeds particularly when it comes to upload at the slingbox hosting residance in Utah. The faster the speed the better the picture and slinging experience. To achieve HD quality picture remotely, you would need a upload of 3.5 meg+ at the slingbox hosting residance.
*Ther basic ule of thumb is the faster the upload at the slingbox location, the better the remote viewing experience.
4. At the remote location, you could watch it on a computer
Hook up a computer to a tv (connection method really depends on your TV's inputs). For example you could hook up a computer (laptop or desktop) to the TV via HDMI, DVI or 15 pin dsub vga conenction if those connections are available.
Puchase the now discontinues sling catcher which was dedicated for just this type of use/experience.