Fix typos and add arguments to a proof

Thanks to Keenan Kidwell
http://stacks.math.columbia.edu/tag/00LO#comment-682
http://stacks.math.columbia.edu/tag/087M#comment-683
http://stacks.math.columbia.edu/tag/00N2#comment-684
http://stacks.math.columbia.edu/tag/00NN#comment-685
http://stacks.math.columbia.edu/tag/00NN#comment-686
http://stacks.math.columbia.edu/tag/00NN#comment-687