I am not familiar with Warpriest, so I cannot speak to 1, 2, or 3.
4) Yes. A net is a weapon, so it can be enchanted as normal for a weapon. This includes both enhancement bonuses and special abilities. You could make a +1 flaming net, which would deal 1d6 fire damage. You would not add the +1 to this damage, however, since the enhancement bonus is applied to damage rolls, and you do not make a damage roll with a net. Since flaming does 1d6 fire damage on a successful hit, it's bonus damage would still apply. You would also add your enhancement bonus on attack rolls.
5) No. Sneak attack deals extra damage, so it could add 1d6 damage to an attack that normally deals 0 damage. However, a net does not deal damage at all (rather than dealing 0 damage), so you cannot add extra damage to it. If Warpriest's sacred weapon ability can grant a net a damage roll, then sneak attack would apply normally.
So the crucial part of the Sacred Weapon ability reads as follows:
Whenever the warpriest hits with his sacred weapon, the weapon damage is based on his level and not the weapon type. The damage for Medium warpriests is listed on Table 1–14; see the table below for Small and Large warpriests. The warpriest can decide to use the weapon's base damage instead of the sacred weapon damage—this must be declared before the attack roll is made. (If the weapon's base damage exceeds the sacred weapon damage, its damage is unchanged.) This increase in damage does not affect any other aspect of the weapon, and doesn't apply to alchemical items, bombs, or other weapons that only deal energy damage.