1) I can't change the month.
2) I tried to enter two category-IDs, but it takes only one. I tried in different ways (no blank after comma, blank after comma).
For me it seems, there are mistakes in the code.
You would try the new version. Categories selection in module is working now as expected.
About changing the month....I'm not sure what you mean. If you want to change the month name/format you have to look in joomla default language file of your language pack, Blog Calendar uses it to take month names and date format.