given: r^n = s^2 = 1, rs = sr^-1, and a = s, b = sr
prove: (ab)^n = 1.
so we must show that (srs)^n = 1. note that since s^2 = 1, s = s^-1. so we are showing that (srs^-1)^n = 1.
but (srs^-1)^n = sr^ns^-1 = ss^-1 (since r^n = 1)
(1 ) you can prove the presentation does generate D2n (how many distinct elements can we have?. which elements are the rotations, and which are the reflections?)
(2) this is what you presumably just showed. since each presentation is derivable from the other, the two groups presented are isomorphic (showing that two isomorphic groups need not have the same presentation, which is part of a much larger problem within group theory).