Please help with HDMi Cables

Certified High Speed HDMI cables are all you need for lengths up to about 25'. Sitlet's link is a good place to start. You can also get high quality cables from MediaBridge and Blue Jeans as well. Don't go with the "M" brand (not to be confused with Sitlet's link)

All hdmi cables are typically the same. If they are rated for ethernet however, that usually means they are up to a higher spec than normal cables.

No. The optical output of the tv ONLY outputs 5.1 from the internal (QAM or antenna) tuner. Anything else connected to it will give you 2 channel. You need to connect the source device directly to your receiver. HDMI is the best connection, as it allows all audio formats. Optical or coaxial digital will only give you 5.1 DD or DTS at best.

If you are not using 3D content from a 3D BR or PS3 player you do not need a High speed cable in fact if less then 15 feet a 22 gauge standard cable is fine even for 3F.
22 gauge is thicker (better)then 14 gauge, not the other way around.
You do not need an HDMI cable to also support Ethernet unless you know you will be also running a Ethernet connection between the two devices in addition to the HDMI connection.

Certified High Speed HDMI cables, with or without ethernet, meet and exceed all current HDMI specs that are currently offered on consumer devices (which use the HDMI 1.4 hardware protocol) and are backwards compatible for devices that are using the HDMI hardware protocol specs earlier than 1.4/1.4a. If they are certified for the length that you are using, that just means they are guaranteed to meet those specs because they've been tested, at that length, and passed. Anybody can make a cable and say they will meet the High Speed specs, but unless you can get a certificate that show they were tested and passed, there's no guarantee. Presently, there are no consumer devices that can take advantage of the ethernet channel in the HDMI cable so that's a future spec, if the mfrs adopt it. Just like 4k. High Speed cables have been able to handle 4k for awhile now but 4k is just starting to become available.

Optical cable is usually used to transmit discrete 5.1 audio from the tv's internal ATSC tuner to the AVR. If the tv is smart, and the smart apps are capable of decoding 5.1, you may be able to get 5.1 audio that way as well if the program offers it. The simplest setup is to have all of your devices connected to the AVR via HDMI and then a single HDMI cable out to the tv. All of your audio is decoded and played thru the AVR with only the video being passed to the tv. Cable boxes can add another dimension to that because there are a couple of ways you can make your connection. Some connect their cable boxes, via coax, directly to the tv's Cable/Ant input and use the tv's internal ATSC tuner to scan and find the cable stations. Then a simple optical out and you've got 5.1 for all of the stations that offer it.

The cable box, from what I understand (I don't have cable, only OTA), can be either connected via coax directly to the tv for video and 5.1 audio via optical out to the AVR or it can be connected directly to the AVR via HDMI. However, in that scenario, you won't get 5.1 out from the tv if you use the optical cable from the tv to the AVR because most tv's can't play true 5.1 via the optical cable from an external HDMI source. I would think that using HDMI from the cable box to the AVR would work but obviously I'm not familiar with connecting cable/sat. What I do is connect everything to the HDMI inputs of my AVR (blu-ray player, AppleTV2) and then have a single HDMI cable out from the AVR to the tv. TV for us is OTA only so I have my antenna connected directly to the tv's Cable/Ant coax input, turn off the tv's speakers, and have the optical cable out from the tv to the optical In of the AVR. All audio sources are played thru the AVR (all formats) with video only (via HDMI out) going to the tv. OTA 5.1 audio is played from the internal ATSC tuner (antenna coax connection) to the AVR via the optical cable. A very basic setup. Everything is controlled with one remote (Harmony) so that single click of a button for whatever I want to do (watch TV, movie, ATV2) turns off or on the appropriate device and selects the correct input.