The answer to this kind of question is almost always printed on the back of the device near the power cord. Look for it.
Not if it is THEIR cable box. You pay to use the box. No pay, no box.
If it is HD, yes.
No, it is made for use with cable only.
A Cable box and TV are connected together through a RF cable.
The cable comes out of the wall to the HD converter box and the converter box connects with the HDMI or video cable to the same on the tv set. If the tv has HDMI connector use it. HDMI will give you much better picture than video cable connections.
You cannot unless it can connect via USB. If it does, you must use it wired. You will have to check your cable box's manual to see of you can.
No. You would need a coaxial (preferably video) cable to connect a cable box to a VCR, unless your cable box has RCA outputs, which most don't.
Yes you can. Just connect it to the cable box, and set it up correctly.
The cable box itself would not be an issue. Cable boxes will not work on their own, there must be a live feed of cable for the box to have channels to choose from. If someone is not paying for that cable to be available at that residence but for whatever reason there is a live feed coming through, it would be seen as illegal.
i don't believe so.
Connect the audio output of the cable box to the input of the home theater system. If both systems have digital connectors, use them.
It's not uncommon. Look to see if your cable box has an antenna input. If it does, it's just a remote click to change from cable to TV. If not, you'll have to use an antenna switcher.