1. Yes. 2. Yes. (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:
if you have 2n edges of your polygon, they will give $n$ edges after gluing,
and suppose that you obtain $v$ vertices after gluing.
Then the Euler characteristic is $1-n+v$ which is between $2-n$ and $2$.

And you see that
for given length there are much
more classes of words than possible values of the Euler characteristic.