I usually have my emblem blank and was dismayed to find that there is no Seventh Column(toggled version is blank)? Or do I have to do some challenge to receive it?
I feel your pain. Ever since emblems were introduced (Halo 2), I have used the blank variant of the seventh column emblem. I personally just don’t like playing with bright, neon, out of place stickers on my Spartan while I’m at “war”. I was disappointed to see that symbols can not be disabled this time around. I’m not sure if this was simply an oversight by 343 or merely an effort to make symbols more prominent, but they still look out of place on Spartans to me. Hopefully they will add the ability to disable emblems in the future, but I’m sure not holding my breath on that one.
I was personally destroyed when I realised I couldn’t put a cowboy hat on my cat emblem 
The seventh column was Bungie’s thing, and I believe they own that particular logo (IP).
The seventh column symbol is property of Bungie.
Also, no star. I’ve used a star as my emblem for 8 years.