Just give the requested example. You do not need to justify that your example has the desired properties.
a) Give an example of a metric space (X, d), an open set E ⊂ X and a sequence (x_n), in E which converges to a point outside of E.
b) Give an example of a bounded set which is not totally bounded.
c) Give an example of a sequence of functions (f_n) which converges pointwise to a continuous function f, but does not converge uniformly to f.
d) Give an example of a power series with radius of convergence 0 < R < + which converges at R but not at -R.
