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Answer 1

$1) \ \dfrac{m-n}{(m+n)^{2} }-\dfrac{2m}{m^{2}-n^{2}}+\dfrac{m+n}{(m-n)^{2} }=\\\\=\dfrac{(m-n)(m-n)^{2}-2m\cdot (m^{2}-n^{2})+(m+n)(m+n)^{2}}{(m-n)^{2}(m+n)^{2}} =\\\\=\dfrac{(m+n)^{3}-2m^{3}+2mn^{2}+(m+n)^{3}}{(m-n)^{2}(m+n)^{2}} =\\\\=\dfrac{m^{3}-3m^{2}n+3mn^{2} -n^{3} -2m^{3}+2mn^{2}+m^{3}+3m^{2}n+3mn^{2} +n^{3}}{(m-n)^{2}(m+n)^{2}}=\\\\=\dfrac{8mn^{2} }{(m^{2}-n^{2} )(m^{2} -n^{2})}$

$2) \ \dfrac{8mn^{2} }{(m^{2}-n^{2})(m^{2}-n^{2} )}:\dfrac{8mn^{2} }{m^{4}-n^{4}} =\\\\=\dfrac{8mn^{2} }{(m^{2}-n^{2})(m^{2}-n^{2} )}\cdot\dfrac{(m^{2} -n^{2})(m^{2}+n^{2}) }{8mn^{2} } =\dfrac{m^{2}+n^{2}}{m^{2}-n^{2}} \\\\\\3) \ \dfrac{m^{2}+n^{2}}{m^{2}-n^{2}} +\dfrac{2n^{2} }{n^{2}-m^{2}} =\dfrac{m^{2}+n^{2}}{m^{2}-n^{2}} -\dfrac{2n^{2} }{m^{2}-n^{2} }=\dfrac{m^{2}+n^{2}-2n^{2}}{m^{2}-n^{2} }=\\\\=\dfrac{m^{2}-n^{2}}{m^{2}-n^{2}}=\boxed1$