By Kanto Area Pass to Echigo Yuzawa

Understand that I can purchase a Gala Option Ticket to extend the coverage of Kanto Area Pass to Gala Yuzawa. I would like to go to Echigo-Yuzawa from Ikebukuro. Is these route covered by Kanto Area Pass + Gala Option?

1. Ikebukuro by JR Shonan-Shinjuku Line(Via Utsunomiya Line) to OMIYA(SAITAMA)

2. From OMIYA(SAITAMA) to Echigo-Yuzawa - I am not sure if Kanto Area Pass only can be used on SHINKANSEN TANIGAWA or it can be used on Max Toki as well.

3. I assume I do not need to go via Tokyo. Omiya is a shorter route as I am going from Ikebukuro. Am I right?

This is the note I captured from JREast.com - "The GALA Option Ticket is valid for a round trip on Ordinary Car reserved seats between Jomo Kogen Station and Echigo-Yuzawa/GALA Yuzawa Station on the Joetsu Shinkansen. (Please note that the GALA Option Ticket is valid only on the Joetsu Shinkansen route.)"

I am not sure what does "Ordinary Car" means. Experts, please enlighten me please. :)

1. Ikebukuro by JR Shonan-Shinjuku Line(Via Utsunomiya Line) to OMIYA(SAITAMA)

Yes, it is a JR line!

2. From OMIYA(SAITAMA) to Echigo-Yuzawa - I am not sure if Kanto Area Pass only can be used on SHINKANSEN TANIGAWA or it can be used on Max Toki as well.

It can also be used on Toki and Max Toki trains, but only if they stop at Echigo-Yuzawa, of course. Several of them do not stop there.

3. I assume I do not need to go via Tokyo. Omiya is a shorter route as I am going from Ikebukuro. Am I right?

Yes, you are right.

I am not sure what does "Ordinary Car" means.

As opposed to "Green Car", the first-class option. Basics are explained here:
http://www.japan-guide.com/e/e2018.html