Here are my questions. First, if I want full HD cable service available on a second TV in another room, would I need to purchase/rent another cable box, or would a single cable box work?
If you want all the hd channels, then yes, you need a cable box or a dvr on every tv. You can however get QAM hd channels, normally just the locals (abc, nbc, fox, cbs) in hd, if your tv supports qam that is.
Also, would there be an additional cost?
For the actual cable subscription? No, whatever you pay for, you pay for the whole house. You will have to pay to rent the extra cable box though.
The phone rep explained that cable can be distributed throughout the house via coax (presumably like dual-tuner Dish Network receivers), but then then it seemed like they were saying that with this configuration, only SD programming would be available on the other sets throughout the house.
What they are saying is, they are not responsible for wiring your house with coax. When they come install, they will install your modem and one tv. After that, you are on your own. However, unless your house is very old, you should have coax in every room. And with the sd thing, they mean that unless you have a cable box in every room, you will only get sd channels on that tv.
They also seemed to imply that with a single receiver, I could have cable service on as many TVs as I wanted throughout the house.
They are confused, as phone reps usually are. What they meant by that is, one receiver works for one tv. You cannot use one cable box with multiple tvs. But again, as long as you have coax in each room, you will get sd channels and hd qam channels.
Also, with HD service, what channel lineup would I receive? On the website, they have Basic, Standard, and Digital Basic categories listed (along with premium channels and packages which I assume cost extra), but there's no
clear indication of what channels are included with their HD service.
That would be something they would have to answer. Although, normally with hd, you will pay for either all HD channels, or none. This is excluding the subscription channels, like HBO and Showtime. But again, that completely depends on how they offer the channels.