Re: The green lantern is a symbol that the restaurant is supporting local farmers.
All of these are okay.
I prefer #2 to have a "that" after "shows" - which gives you "that shows that" but that's okay.
I tried asking myself the question "Hey, what does that green lantern mean?" and when I answered myself as spontaneously as possible, I didn't use "a symbol."
The green lantern shows that the...
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.