What does the ‘Confidence’ stat mean in Endless Legend

The bonus is multiplied by the number of pacified villages within your empire. This can easily be seen by pacifying 1 of 2 villages in a region you control and assimilating them. If you check the appropriate bonus immediately before and after pacifying the second you'll see it go up. This can make it worthwhile to assimilate a minor faction that is present in multiple regions to get a 3+ multiplier on your benefit.

The bonus applies to every unit you own, it is not applied when the unit is built. Unless of course it's a City or Army bonus.

I don't know the specifics of Cultist Assimilation

The wiki says this:

Every winter is longer than the one before, and adds one new penalty (written in red at the beginming of the winter).

I couldn't find any consistent information about winter duration, but I read that after you won the game, the winter becomes eternal. It is by design.