It counts towards absolutely everything except for adding your name to the specifics games leaderboard (such as tranzit 1,2,3,4 - bus depot survival/grief(if your a pimp) - town survival/grief, farm survival/grief). So getting to round 80 on survival in custom mods wont show you got to round 80.
Yes it counts. You need to not touch any game rules like "Hellhouds - on". If you put it on easy, only kills/deaths will count ^_^