1 - Depends on your internet connection speeds:
- Upload speed at the place your SlingBox will be (You need at least 2Mb/s upload speeds for HD to even work, closer to 3Mb/s for it to be smooth & sharp.)
- Download speed at your college: Must be equal to or greater than your upload speed at home. If you are on a college's residential network, they are pretty good at clamping down on specific types of internet traffic, this may/may not affect your video streaming capabilities, (Best way to figure this out without buying the SlingBox is to connect to someone else's SlingBox (if you know someone that has one) at your college and see how it does.)
2 - The SlingBox Pro HD looks great on HDTV's when your connection speeds are sufficient.
3 - It doesn't matter if you are connected using Ethernet or WiFi, both are more than sufficient to stream HD video.
4 - You'll either need a SlingLink to connect your SlingBox to your router in the other room or find a way to run a long Ethernet cable to it (you can pick up cheap Cat5e or Cat6 Ethernet by the foot on the internet or at a hardware store, you just have to buy the "ends" and crimp them on yourself.
5 - Yes, again provided your connection speeds are good enough for whether you're watching something in SD or HD.
Hope that helps! :-)
The Slinglinks use the house's electrical wires to transfer the video/audio signals from one Slinglink (connected to your router) to the other Slinglink (connected to your Slingbox). There is a description of the setup at http://www.testfreaks.com/blog/review/slinglink-turbo-single-port/
One potential problem, however, is that both slinglinks must be connected to electrical outlets that are on the same phase of the home's electricity or they won't be able to communicate with each other. Most homes have two phases -- open the main circuit breaker panel door and you will typically see two rows of circuit breakers, which represent the two phases. So, if the electrical outlet where you connect the Slinglink next to your router is not on the same phase as the electrical outlet where you connect the Slinglink next to your Slingbox, then they won't be able to communicate with each other and you would have to do some rewiring in the circuit breaker panel -- not for amateurs! -- or find another electrical outlet that IS on the same phase.
As an alternative to the Slinglink approach (if you can't run an ethernet cable between your router and the slingbox (which would be the best approach as noted above), then you could purchase a wireless access bridge and install it near the Slingbox, then plug connect and Ethernet cable from the wireless access bridge to the Slingbox.