Is it possible (somehow) to have in Git (local) relative revision (commit) numbers, like in Mercurial 0, 1, 2, 3, ... instead of short hashes?
Short answer: No. Yes.
However, you could use git-tag. For example, to tag your latest commit as version 1.2 do something like:
git tag -a v1.2 HEAD
This page explains how to use it for versioning: http://grinninggecko.com/commit-version-numbers-with-git/