Let's say I have 3 Elven warships and a shadow warrior in play at the start of my turn. My opponent has a unit with toughness 5 in his battlefield. If he decides to allocate all of the warship indirect dmg and the 1 dmg from the shadow warrior to his unit with toughness, how does that work. It all happens in the start of the turn action window so is it simultaneous? Or does that "actions function independant of their source once activated" mean that he can use toughness against each group on incomming dmg one at a time?

Hmm, it seems you are confused about a few things.

First of all, the fact that effects, once triggered, exist independently of their source doesn't have anything to do with this scenario. It just means that if you trigger the action of your Elven Warship, and I respond to that by destroying your Warship, the effect will still resolve.

Elven Warship's effect is an Action, that of Shadow Warrior is a Forced effect. Forced effects are resolved before actions, so your opponent deals 1 damage to a unit in his battlefield. Note that this isn't indirect damage. Indirect damage is always called indirect damage, and it can be distributed freely among all your units, legend, and capital zones.

After the Forced effect has resolved, you can start an action chain. So you start the chain with the action of any one Warship, and assuming your opponent doesn't do anything, respond to it with the action of one of the other two Warships, and then with the third's. Then the chain is resolved in reverse order (which really doesn't make any difference in this case, since it's all the same).

So assuming you indeed choose to assign all the damage to that one unit, it gets dealt 1 damage from the Warrior's effect, then three times 2 damage from the Warships' effects. If it has at least Toughness 2, the toughness will cancel all that damage. Separate effects always stay separate, you don't add up the results - technically, though in actual play it often is perfectly all right to do so, just not in cases like this. The units gets dealt damage four times, 1 + 2 + 2 + 2, not one batch of 7 damage in one go, not 1 and then 6 in one batch.

Alright then. Thanks a lot for taking the time to clarify this.