Although uncommon, it is possible that his grandmother's DNA did not get passed down to him. If his siblings are still alive, try testing them. If they are not alive, try testing some of his nieces and nephews.
Autosomal DNA cannot separate the contribution between the father and mother. You will need to compare results from other lines for that and you will have to do it yourself. You and other relatives will need to download your DNA results from here and upload to GEDMATCH (free) or FTDNA (not free) to use their tools to see how the chromosomes layout.
Y-DNA can only determine relationships father to son throughout generations in the direct male line descent.
You cannot go by looks in a picture. There were some groups in other parts of the world that looked very much like American Indians. In addition some American Indians are showing results more typical of Asiatics on their genetic results.
I think I've read that there was a special recording of Indians in addition to or apart from the censuses so you might look into that.
It is also a sad fact that it takes very little to start that American Indian story in a family. It's easy to go from "he/she looks like an Indian" to "he/she was an Indian". In one family, it started because an ancestor lived on Indian Creek.