Do i need a HDMI cable?

This will depend on your home theater. Most home theater in a box are not flexible for you to add anything or for upgrading. They are mainly designed for you to watch a movie with surround sound with the built in dvd or blu ray disc player. A receiver is a much better choice for this. Keep in mind that your tv will only have an optical audio output. This is a digital signal that has to be decoded. HDMI cable carries the video and audio signal in one cable. You should connect your cable provider directly to the tv and then connect an optical audio cable from the tv to the home theater. Hope this will help you out.

Only if your sound system has HDMI input. Otherwise, you have to connect optical cable from cable box or TV to sound system for TV channel audio.

You don't need one, you want one. There are a couple audio protocols available to connect your equipment, I'm sure. However, the beauty of the HDMI is it's all inclusive capability, coupled with its simplicity. HDMI carries all available audio signals, compressed and uncompressed, up to Dolby Digital 7.1, as well as DVI digital high definition video, and a little data on the side. (some electronics utilize the data capability for easier control of functions) I'd run HDMI directly from your cable box to your theater, and either from your theater to the tv, or another from your cable box to the television. You'll get the most of your equipment's ability, no compromise, and easy two cable hookup. You don't even have to worry about getting left, right, front, back, center, sub, etc. mixed up.

Probably. This cable will allow the full HD experience. If the tv is wall mounted, with wires in the wall, use a HDMI cable that is wall rated. More expensive yes, but it is designed to be there. UL-rated.