In theses [these notes][1], Example 5.6, it is said that there is a "symmetric tiling of a genus 2 surface by 8 right-angled hyperbolic heptagons".
 
Question 1: What does this tiling look like?

Question 2: Is it always possible to tile a genus $n$ surface by $f$ regular $n$-gons with interior angle $\pi/v$ (so that $v$ faces meet at every vertex) as long as the restriction given by the Euler characteristic 
$$\chi=2-2n= f-nf/2+nf/v$$
is satisfied?
Answering [this question][2], Igor Rivin says yes, but it seems his argument only shows that regular hyperbolic $n$-gons of interior angle smaller than the interior angle of a euclidean regular $n$-gon exist.


  [1]: https://www.dpmms.cam.ac.uk/~hjrw2/Notes/cubenotes.pdf
  [2]: https://mathoverflow.net/questions/198040/regular-tiling-of-a-surface-of-genus-2-by-heptagons?r=searchresults