Does Grand Floridian give military discounts?

Yes i think so

I think so

Yes

Disney offers military discounts at all resorts. Here is a link to details which includes limitations. https://disneyworld.disney.go.com/special-offers/military-hotel-rates-2019/details/

Shades of Greens is for Military personnel

They seem quite accommodating, I would guess yes but give them a call. Disney magic!