The essence of the problems you posted is understanding definitions.

A point is interior to a set if some open set containing the point is a subset of the set. An intuitive way to look at it is: a point is interior if every point close to it is also interior. Note too the existential, some open set.

On the other hand, a point is a boundary point ifevery open setcontaining the point also contains a point in the set and a point not in the set. That is: every open set about the point intersects both the set and its complement.

Therefore, no interior point can be a boundary point and visa versa.

Thus it is easy to apply definitions to prove

You may also learn some things by viewing the LaTeX.

It really is best to learn to code.