- Yes. 2. No. (I suppose that the surfaces are distinct if they are homeomorphic).
For 1, it is sufficient to check the definition of surface: that every point has a neigborhood homeomorphic to the disc. For interior points of the polygon, and for points on the sides, this is evident, and for the corners this is easy.
For 2, just recall classification of all possible compact surfaces up to homeomorphism. There is one integer invariant, the Euler characteristic. The Euler characteristic is easily computed from your word, and you see that for given length there are more classes of words than possible values of the Euler characteristic.