Slitherine

Do villages on hills get any benefits in combat? ie do they get to count as uphill?

In a villages is assaulted across a river does this affect combat?

if a village is uphill I don't see why the defenders can't claim an uphill bonus.

Not sure how a river would affect a unit that tries to assault a village from across a river. Don't forget some river depths prevent assaults. I would guess if you are disordered while in the river then you would lose a die assaulting the village. Stick to the ones on dry land, the property values are higher as there is less flood damage

This is not mentioned in the Buildings FAQ. It says that flank support does not apply, and that rear support does and explains the situation in which it does.
I think these two are mentioned because they are both "support", but only one applies.

However, in the rules on p.77 (LH column, 5th bullet) it states that - All other factors that may change the number of dice rolled are ignored, other than normal the normal reductions for cohesion losses.
Considering that the rules for combat against defended buildings in the FAQ seem to be a clarification of the RAW, rather than a replacement, I think this bullet point applies.

As for assaulting a town across a river, I would apply the penalties on the attackers as they are listed on p.79, but no other effect on the defender - i.e. cohesion losses for the attacker depending on the size of the river/stream.

I agree any disorder applies to the attacker in the river only. building defenders get full dice.