The action it takes to drain the river is equivalent to the action it takes to attack across it;
If you drain before attacking, you save yourself one guy. If I read the combat rules correctly, that is.
No, I don't think so.
Take over a neighbouring contested territory. This costs +1 extra action per defence of terrain. Both the conquered region and the conquerers lose 1 population, to a minimum of 1. All fields and fortifications in the conquered hex are destroyed.
Rivers
Colour: Light Blue
Defence: +1 when conquering civilisation has to cross the river to enter the hex
The population loss is a flat 1 pop per territory conquered. You can either use one action to drain the river and then attack, or not drain the river and use one action to get over the +1 defense afforded by the river. Quite frankly, it's more advantageous to leave the river there so that the Merfolk can't counter-conquer back into your original territory.
the enemy is slowed the same, and it doesn't save them all that much.
Yes, but if you drained a border river, you were probably going to attack the same turn, and thus were probably going to take this tile.
No probably about it; the combat is completely deterministic. The tile is definitely taken if the enemy is willing to pay the price; the river makes it more expensive to attack, which serves as a deterrent and gives you an edge in the action economy. Consider the following:
Aquatic owns a border plains with a fortification and a defensive river on the enemy side; conquering this tile takes 3 actions for the enemy, one for the conquer action, one for the fort and one for the defense of the river. Successfully conquering the tile eliminates the fortifications. The Aquatic turn comes up for a counterattack, and they only have to invest 1 action in taking it back; there is no fort, and there is no river on their side; if the enemy drained the defensive river, then the Aquatic have the option of using their extra action to return things to the status quo (and since they're the only ones who can Channel, they're the only ones who can make this choice,) or to continue attacking into their neighbor's territory.
Obviously if it's winter the enemy can invest another action in trying to fortify their new holdings to make it more expensive for the Aquatic to counterattack, but that just means the enemy needs to invest 4 actions to take and hold their tile while the Aquatic player just needs 2 to take it back; the gap is the same. The point is that it takes an extra action for the enemy to be aggressive, and there's effectively a 2 action swing depending on how well prepared the Aquatic player is, narrowing (or widening, if the enemy is foolish and the Merfolk are already on the + side of that equation) the action deficit.