part a
it can't be a time invariant because output is not same.
$ X_k[n] = \delta[n-k] $
$ \delta[n-k]\rightarrow time delay\rightarrow\delta[n-k-n_0]\rightarrow system \rightarrow (k+n_0+1)^2\delta[n-(k+n_0+1)] $
$ \delta[n-k]\rightarrow system \rightarrow Y_k[n] \rightarrow time delay \rightarrow (k+1)^2\delta[n-(k+n_0+1)] $
