New Pic, 1921 Morgan Dollar.

First, the obverse has the date on it, the reverse has the motto on it

I don't see a die gouge above the G, could be the glare. If you mean the chip/crack at the top of the G (where the back serif meets the front serif) that is fairly common, but some are more pronounced than others. Yours seems like a midline chip/crack (not real big , but not real small)

There are alot of Doubled dates on these coins, I don't think I own a 21 that does not have some doubling on the obverse, most including the date. Hard to tell from the pics...glare again..but I will go out on a limb and say yes it is doubled.

A couple of picture hints...try to always rotate your pictures to the upright position, the eye recognizes things better in their correct orientation. Also you might tweak the brightness down a bit, or reduce the highlights and up the contrast a little. Play around a bit with them until you think we can see what you see, otherwise it is very tough to give you definitive information. Also, pictures of the entire coin along with the close-ups can be helpful for these since die cracks can be a good starting point to find the VAM information . Dontcha just love the 21's........